According to Robert Millet, for Corianton to "cross himself" (Alma 39:9) was for him to turn away from evil inclinations, to deny himself of worldly lusts, to work at cross purposes from the natural man, to forsake worldly paths, and to chart and navigate a course of righteousness. (See 3 Nephi 12:30) [Robert L. Millet, "The Path of Repentance," in Studies in Scripture: Book of Mormon, Part 2, p. 51]
“Cross Yourself”
According to Daniel Ludlow, the meaning of the expression "cross yourself" (Alma 39:9) is clarified in other scriptures. For example, 3 Nephi 12:30 says: "For it is better that ye should deny yourselves of these things, wherein ye will take up your cross, than that ye should be cast into hell." In Matthew 16:24 the Savior says, "If any man will come after me, let him deny himself, and take up his cross, and follow me." Both of these scriptures indicate that to "cross yourself" means to deny yourself. In the [Joseph Smith Translation] of the New Testament the Savior makes it absolutely clear that this is the meaning of the term: "And now for a man to take up his cross, is to deny himself all ungodliness, and every worldly lust, and keep my commandments" (Matthew 16:26). [Daniel H. Ludlow, A Companion to Your Study of the Book of Mormon, p. 223]