After the Fall, the Lord declared unto Adam: “Cursed is the ground for thy sake” (Genesis 3:17; see also Moses 4:23). It is clear from other scriptural commentary (see Moses 5:10-11), that this original “cursing” of the land, as a result of the Fall, was a beneficial act that provided for the growth and development of Adam and Eve and their posterity, as well as allowing for the full operation of the plan of salvation.
In contrast to this usage of the phrase “for their sake,” Mormon uses the phrase not to illustrate any beneficial aspects but rather to point out another terrible consequence of the wickedness of his people. The definition of “sake” in an 1830 dictionary or some other contemporary edition would include “on account of.”
This definition seems to fit better with Mormon’s intent and is consistent with other Book of Mormon passages that use similar language. The land was “cursed” not for the blessing or benefit of the Nephites in any way, but rather “on account of” their great wickedness. See 2 Nephi 1:7; Alma 45:10-16; Ether 2:8-12.