And the uncircumcised man child whose flesh of his foreskin is not circumcised, that soul shall be [Hebr. karath] from his people; he hath broken my covenant. (Genesis 17:14)
The Mosaic covenant describes the same consequence. From Exodus to Deuteronomy there are all kinds of laws that come with a warning that those who break them will be cut off from the people, whether it is breaking the sabbath, touching unclean things, eating blood, eating sacrificial meat reserved for the priests, not keeping the passover, etc. In each case, being cut off is the consequence of breaking the covenant they have cut.
In the Book of Mormon, "cut off" is part of the standard phrase that I have called the Book of Mormon proverb.
as ye shall keep my commandments ye shall prosper in the land; and inasmuch as ye will not keep my commandments ye shall be cut off from my presence. (2 Nephi 4:4)
This post explains that this is a metalepsis of the Mosaic covenant as outlined in Deuteronomy in particular. The Nephites have the same covenant terms and consequences as their fathers.
It is interesting to note how this applies both on a personal and collective level. Individuals who broke the covenant were cut off from the people. But when the people of Israel by and large had fallen into apostasy, their kingdom was cut in half and split into a northern and southern kingdom. After that, they were cut off from the promised land and the temple (and thereby cut off from the Lord's presence) as prophesied by King Solomon
6 But if ye shall at all turn from following me, ye or your children, and will not keep my commandments and my statutes which I have set before you, but go and serve gods, and worship them:
7 Then will I Israel out of the which I have given them; and this house, which I have hallowed for my name, will I cast out of my sight; and Israel shall be a proverb and a among all people (1 Kings 9)
Ezekiel also talks about a sword going through the land cutting off Israel
Or if I bring a upon that land, and say, Sword, go through the land; so that I cut off man and beast from it (Ezekiel 14:17)
This all made me think of Nephi's vision. He sees, like his father saw, a gulf separating the righteous from the wicked, or the tree of life from the great and spacious building.
And the large and spacious , which thy father saw, is vain and the of the children of men. And a great and a terrible divideth them; yea, even the word of the of the Eternal God, and the Messiah who is the Lamb of God, of whom the Holy Ghost beareth record, from the beginning of the world until this time, and from this time henceforth and forever. (1 Nephi 12:18)
Royal Skousen has postulated, quite convincingly in my opinion, that the "word" in this verse should have been "sword". This was simply a typo by Oliver Cowdery when copying from the original manuscript to the printer's manuscript. Nephi explains to his brothers:
28 And I said unto them that it was an awful , which separated the wicked from the tree of life, and also from the saints of God.
29 And I said unto them that it was a representation of that awful , which the angel said unto me was prepared for the wicked.
30 And I said unto them that our father also saw that the of God did also divide the wicked from the righteous; and the brightness thereof was like unto the brightness of a flaming , which ascendeth up unto God forever and ever, and hath no end. (1 Nephi 15)
This gulf, representing a division or separation, is caused by the "sword of the justice of the Eternal God" with "brightness of a flaming fire". I believe that this wording would create certain vivid images in the mind of an ancient Israelite. One is the flaming sword with the cherubim guarding the way to the tree of life, that Lord Wilmore discussed here, and Adam and Eve who were "cut off from the tree of life" (Alma 42:6). Another is the sword that cuts the animals in half whenever a covenant is made, symbolizing the consequences of breaking the covenant. The divine sword that cut Israel also ultimately creates the gulf by cutting off the wicked from the tree of life. So there is a covenant setting to Lehi's dream as well. This is not far fetched at all. After Nephi's vision, his brothers quarrel over the words of their father. Nephi, who had just seen what his father saw, explains
18 Wherefore, our father hath not spoken of our seed alone, but also of all the house of Israel, pointing to the covenant which should be fulfilled in the latter days; which covenant the Lord made to our father Abraham, saying: In thy shall all the kindreds of the earth be .
19 And it came to pass that I, Nephi, spake much unto them concerning these things; yea, I spake unto them concerning the of the Jews in the latter days. (1 Nephi 15)
This is just before he goes on to tell about the gulf a few verses later. The restoration of the Jews in the latter days results in a modern Israel of which we are part. Only those who keep their covenants will not be cut off from the tree of life.