As part of the sacrament covenant prayer, we find the following reference to symbolically drinking the blood of Christ:
The manner of administering the wine--Behold, they took the cup, and said: O God, the Eternal Father, we ask thee, in the name of thy Son, Jesus Christ, to bless and sanctify this wine to the souls of all those who drink of it, that they may do it in remembrance of the blood of thy Son, which was shed for them; that they may witness unto thee, O God, the Eternal Father, that they do always remember him, that they may have his Spirit to be with them. Amen (Moroni 5:1-2)
According to John Welch, although the idea of ceremonially drinking wine as a symbol of blood may have been new to the Nephites, and while the eating or drinking of blood was almost certainly taboo among righteous Nephites (see Jarom 1:6), as it was among the Israelites generally (see Genesis 9), the Nephites may have known something of the idea of drinking blood in connection with making vows. The drinking of blood or the symbolic use of blood in covenant making and in uniting with the gods has a widespread history among many cultures, notably in ancient Mesoamerica. Perhaps blood was involved in the making of certain oaths in the Book of Mormon: Amalickiah swore an oath that he would drink Moroni's blood (Alma 49:27; 51:9); Giddianhi swore an oath that he would annihilate the Nephites (3 Nephi 3:8) and then led his armies "dyed in blood" (3 Nephi 4:7). The role of blood symbolism here deserves further investigation. [John W. Welch, "Benjamin's Covenant as a Precursor of the Sacrament Prayers," in King Benjamin's Speech: "That Ye May Learn Wisdom," p. 314]