What is the purpose of baptism, and what does Nephi say will cause the remission of sins? Latter-day Saint scholar Noel B. Reynolds has written an exhaustive analysis of the language that is used to describe the baptismal covenant throughout the Book of Mormon. Interestingly, he found that the Book of Mormon never talks about baptism as washing away our sins.
The purpose of baptism is not so much to wash something away, and that especially makes sense when we baptize eight-year-old children who have no sins. After all, why would we baptize them to wash away non-existent sins? More fundamentally, this ordinance is mainly about the commitment to keep the commandments and witnessing to Heavenly Father, that you will keep the covenants that you have made. And then, when the baptismal covenant is renewed with the partaking of the sacrament, the remembrance of the forgiveness of sins is also relived.
The Holy Ghost is then what purges and washes impure things away, the baptism of fire that brings forth the remission of sins. It is much like the sacrifices of the temple in Israel, where burnt offerings were the offerings of atonement that would bring one back into good standing with the Lord. It was the fire that was able to remove impurities.
Book of Mormon Central, "What is the Purpose of Baptism in the Book of Mormon? (2 Nephi 31:6–7)," KnoWhy 59 (March 22, 2016).
Noel B. Reynolds, "Understanding Christian Baptism through the Book of Mormon," BYU Studies Quarterly 51, no. 2 (2012): 3–37.