Baptism does not wash your sins away, it is a "Covenant of  Obedience" Which when faithful to that covenant of Obedience the baptism of the Holy Ghost and the baptism of Fire may be received which then cleanses from sins.  The phrase "baptism unto the remission of sins" or "baptism for the remission of sins"  is as it states,  you must be baptized before you can receive the companionship of the Holy Ghost which does the cleansing.  As the sacrament is the renewal of the Covenant of Baptism, which is that we 1) eat in remembrance of the body of Christ, 2) as a witness to God that  3) take upon the name of Christ (which is obedience)  4) always remember him 5) keep his commandments to 6) receive the spirit which cleanses us.  These things can be seen in the scriptures below as they are "carefully"  read.

2 Nephi 31:5

5 And now, if the Lamb of God, he being holy, should have need to be baptized by water, to fulfil all righteousness, O then, how much more need have we, being unholy, to be baptized, yea, even by water!

2 Nephi 31:Verse 6

6 And now, I would ask of you, my beloved brethren, wherein the Lamb of God did fulfil all righteousness in being baptized by water?

2 Nephi 31:Verse 7

7 Know ye not that he was holy? But notwithstanding he being holy, he showeth unto the children of men that, according to the flesh he humbleth himself before the Father, and witnesseth unto the Father that he would be obedient unto him in keeping his commandments.

2 Nephi 31:Verse 13

13 Wherefore, my beloved brethren, I know that if ye shall follow the Son, with full purpose of heart, acting no hypocrisy and no deception before God, but with real intent, repenting of your sins, witnessing unto the Father that ye are willing to take upon you the name of Christ, by baptism--yea, by following your Lord and your Savior down into the water, according to his word, behold, then shall ye receive the Holy Ghost; yea, then cometh the baptism of fire and of the Holy Ghost; and then can ye speak with the tongue of angels, and shout praises unto the Holy One of Israel.

2 Nephi 31:Verse 14

14 But, behold, my beloved brethren, thus came the voice of the Son unto me, saying: After ye have repented of your sins, and witnessed unto the Father that ye are willing to keep my commandments, by the baptism of water, and have received the baptism of fire and of the Holy Ghost, and can speak with a new tongue, yea, even with the tongue of angels, and after this should deny me, it would have been better for you that ye had not known me.

2 Nephi 31:Verse 17

17 Wherefore, do the things which I have told you I have seen that your Lord and your Redeemer should do; for, for this cause have they been shown unto me, that ye might know the gate by which ye should enter. For the gate by which ye should enter is repentance and baptism by water; and then cometh a remission of your sins by fire and by the Holy Ghost.

Mosiah 18:Verse 10

10 Now I say unto you, if this be the desire of your hearts, what have you against being baptized in the name of the Lord, as a witness before him that ye have entered into a covenant with him, that ye will serve him and keep his commandments, that he may pour out his Spirit more abundantly upon you?

Mosiah 18:Verse 13

13 And when he had said these words, the Spirit of the Lord was upon him, and he said: Helam, I baptize thee, having authority from the Almighty God, as a testimony that ye have entered into a covenant to serve him until you are dead as to the mortal body; and may the Spirit of the Lord be poured out upon you; and may he grant unto you eternal life, through the redemption of Christ, whom he has prepared from the foundation of the world.

Mosiah 21:Verse 33

33 And it came to pass that king Limhi and many of his people were desirous to be baptized; but there was none in the land that had authority from God. And Ammon declined doing this thing, considering himself an unworthy servant.

Mosiah 21:Verse 34

34 Therefore they did not at that time form themselves into a church, waiting upon the Spirit of the Lord. Now they were desirous to become even as Alma and his brethren, who had fled into the wilderness.

Mosiah 21:Verse 35

35 They were desirous to be baptized as a witness and a testimony that they were willing to serve God with all their hearts; nevertheless they did prolong the time; and an account of their baptism shall be given hereafter.

Alma 7:Verse 15

15 Yea, I say unto you come and fear not, and lay aside every sin, which easily doth beset you, which doth bind you down to destruction, yea, come and go forth, and show unto your God that ye are willing to repent of your sins and enter into a covenant with him to keep his commandments, and witness it unto him this day by going into the waters of baptism.

3 Nephi 9:Verse 20

20 And ye shall offer for a sacrifice unto me a broken heart and a contrite spirit. And whoso cometh unto me with a broken heart and a contrite spirit, him will I baptize with fire and with the Holy Ghost, even as the Lamanites, because of their faith in me at the time of their conversion, were baptized with fire and with the Holy Ghost, and they knew it not.

3 Nephi 9:Verse 21

21 Behold, I have come unto the world to bring redemption unto the world, to save the world from sin.

3 Nephi 9:Verse 22

22 Therefore, whoso repenteth and cometh unto me as a little child, him will I receive, for of such is the kingdom of God. Behold, for such I have laid down my life, and have taken it up again; therefore repent, and come unto me ye ends of the earth, and be saved.

3 Nephi 12:Verse 2

2 And again, more blessed are they who shall believe in your words because that ye shall testify that ye have seen me, and that ye know that I am. Yea, blessed are they who shall believe in your words, and come down into the depths of humility and be baptized, for they shall be visited with fire and with the Holy Ghost, and shall receive a remission of their sins.

3 Nephi 18:Verse 10

10 And when the disciples had done this, Jesus said unto them: Blessed are ye for this thing which ye have done, for this is fulfilling my commandments, and this doth witness unto the Father that ye are willing to do that which I have commanded you.

3 Nephi 18:Verse 11

11 And this shall ye always do to those who repent and are baptized in my name; and ye shall do it in remembrance of my blood, which I have shed for you, that ye may witness unto the Father that ye do always remember me. And if ye do always remember me ye shall have my Spirit to be with you.

3 Nephi 18:Verse 12

12 And I give unto you a commandment that ye shall do these things. And if ye shall always do these things blessed are ye, for ye are built upon my rock.

3 Nephi 27:Verse 20

20 Now this is the commandment: Repent, all ye ends of the earth, and come unto me and be baptized in my name, that ye may be sanctified by the reception of the Holy Ghost, that ye may stand spotless before me at the last day.

Mormon 7:Verse 10

10 And ye will also know that ye are a remnant of the seed of Jacob; therefore ye are numbered among the people of the first covenant; and if it so be that ye believe in Christ, and are baptized, first with water, then with fire and with the Holy Ghost, following the example of our Savior, according to that which he hath commanded us, it shall be well with you in the day of judgment. Amen.

Moroni 6:Verse 1

1 AND now I speak concerning baptism. Behold, elders, priests, and teachers were baptized; and they were not baptized save they brought forth fruit meet that they were worthy of it.

Moroni 6:Verse 2

2 Neither did they receive any unto baptism save they came forth with a broken heart and a contrite spirit, and witnessed unto the church that they truly repented of all their sins.

Moroni 6:Verse 3

3 And none were received unto baptism save they took upon them the name of Christ, having a determination to serve him to the end.

Moroni 6:Verse 4

4 And after they had been received unto baptism, and were wrought upon and cleansed by the power of the Holy Ghost, they were numbered among the people of the church of Christ; and their names were taken, that they might be remembered and nourished by the good word of God, to keep them in the right way, to keep them continually watchful unto prayer, relying alone upon the merits of Christ, who was the author and the finisher of their faith.

Moroni 8:Verse 25

25 And the first fruits of repentance is baptism; and baptism cometh by faith unto the fulfilling the commandments; and the fulfilling the commandments bringeth remission of sins;

Moroni 8:Verse 26

26 And the remission of sins bringeth meekness, and lowliness of heart; and because of meekness and lowliness of heart cometh the visitation of the Holy Ghost, which Comforter filleth with hope and perfect love, which love endureth by diligence unto prayer, until the end shall come, when all the saints shall dwell with God.

D&C 20:Verse 37

37 And again, by way of commandment to the church concerning the manner of baptism--All those who humble themselves before God, and desire to be baptized, and come forth with broken hearts and contrite spirits, and witness before the church that they have truly repented of all their sins, and are willing to take upon them the name of Jesus Christ, having a determination to serve him to the end, and truly manifest by their works that they have received of the Spirit of Christ unto the remission of their sins, shall be received by baptism into his church.

D&C 20:Verse 41

41 And to confirm those who are baptized into the church, by the laying on of hands for the baptism of fire and the Holy Ghost, according to the scriptures;

D&C 20:Verse 75

75 It is expedient that the church meet together often to partake of bread and wine in the remembrance of the Lord Jesus;

D&C 20:Verse 77

77 O God, the Eternal Father, we ask thee in the name of thy Son, Jesus Christ, to bless and sanctify this bread to the souls of all those who partake of it, that they may eat in remembrance of the body of thy Son, and witness unto thee, O God, the Eternal Father, that they are willing to take upon them the name of thy Son, and always remember him and keep his commandments which he has given them; that they may always have his Spirit to be with them. Amen.

D&C 33:Verse 11

11 Yea, repent and be baptized, every one of you, for a remission of your sins; yea, be baptized even by water, and then cometh the baptism of fire and of the Holy Ghost.

D&C 39:Verse 6

6 And this is my gospel--repentance and baptism by water, and then cometh the baptism of fire and the Holy Ghost, even the Comforter, which showeth all things, and teacheth the peaceable things of the kingdom.

D&C 39:Verse 10

10 But, behold, the days of thy deliverance are come, if thou wilt hearken to my voice, which saith unto thee: Arise and be baptized, and wash away your sins, calling on my name, and you shall receive my Spirit, and a blessing so great as you never have known.

D&C 68:Verse 25

25 And again, inasmuch as parents have children in Zion, or in any of her stakes which are organized, that teach them not to understand the doctrine of repentance, faith in Christ the Son of the living God, and of baptism and the gift of the Holy Ghost by the laying on of the hands, when eight years old, the sin be upon the heads of the parents.

D&C 76:Verse 51

51 They are they who received the testimony of Jesus, and believed on his name and were baptized after the manner of his burial, being buried in the water in his name, and this according to the commandment which he has given--

D&C 76:Verse 52

52 That by keeping the commandments they might be washed and cleansed from all their sins, and receive the Holy Spirit by the laying on of the hands of him who is ordained and sealed unto this power;