During his ministry (and obviously before He had to bear a physical cross), the Savior said, If any man will come after me, let him deny himself, and take up his cross, and follow me (Matt 16:24). Familiar with images of the scourged Christ bearing the cross on which he was to be lifted for crucifixion, the injunction to "take up the cross of Christ" has suggested the need to withstand the burdens and persecutions we are called to bear as Christians. This is the correct interpretation when we take up His cross. As Jacob taught, we are to view his death, and suffer his cross and bear the shame of the world (Jacob 1:8, italics added).
But the scripture in question is not talking about taking up the cross of Christ but that every individual is to take up his own individual cross. Joseph Smith explained what this means, And now for a man to take up his cross, is to deny himself all ungodliness, and every worldly lust, and keep my commandments (JST-Matt 16:24). It is in this context in which the phrase is used here (3 Nephi 12:30). As Alma counseled Corianton, go no more after the lusts of your eyes, but cross yourself in all these things (Alma 39:9). Therefore, in order for us to be true disciples of Christ, we must first take up our own crosses and deny ourselves of all ungodliness. Then we will be worthy to take up His cross without hypocrisy and without guile (see Matt 10:38).