Matthew 16

To His disciples, the Savior said -

"If any man will come after me, let him deny himself, and take up his cross, and follow me." (New Testament | Matthew 16:24)

Some have interpreted that to mean that we should also bear the cross of the cruxificion as he did. That doesn't make sense because even at this time, that would have meant nothing to His disciples.

I believe the term "take up his cross" suggest checking oneself or as the Savior said "deny" yourselves. We see this in other scriptural quotes -

The Savior said to the Nephites -

"Behold, I give unto you a commandment, that ye suffer none of these things to enter into your heart;
30 For it is better that ye should deny yourselves of these things, wherein ye will take up your cross..." (Book of Mormon | 3 Nephi 12:29 - 30)

Or in other words -

"Yea, come unto Christ, and be perfected in him, and deny yourselves of all ungodliness; and if ye shall deny yourselves of all ungodliness, and love God with all your might, mind and strength, then is his grace sufficient for you, that by his grace ye may be perfect in Christ; and if by the grace of God ye are perfect in Christ, ye can in nowise deny the power of God." (Book of Mormon | Moroni 10:32)

The Joseph Smith Translation footnote states -

JST Matt. 16:26 "And now for a man to take up his cross, is to deny himself all ungodliness, and every worldly lust, and keep my commandments."
(New Testament:Matthew 16:24)