The cuttings and marks in Leviticus 19:28 were associated with heathen practices and the Jews were forbidden to take part in it in order to remain set apart from them.
Since the New Testament does not address the issue of tattooing specifically, one must be guided by principle. Any practice that is vulgar, gaudy, or a distraction to one’s Christian influence should be avoided. But, to some extent, this is a matter of taste and judgment. No one can presume to prescribe conduct for everyone else in matters of this nature. Is it appropriate for women to wear make-up? How about permanent eye-liner? May men and women adorn themselves with jewelry? May they pierce their ears? Christians must attempt to employ sound judgment in such matters, and give no occasion to the adversary for reviling (1 Timothy 5:14). Moreover, a Christian’s personal privacy and right of choice must be respected in ambiguous areas of judgment.
In the New Testament we read that our bodies are not our own. This teaching is found specifically in 1 Corinthians 6:12-20:
“The body is meant for the Lord” 1 Corinthians 6:13.
“Your body is a temple of the Holy Spirit.” 1 Corinthians 6:19.
“You are not your own; you were bought at a price.” 1 Corinthians 6:19.
“Honor God with your body.” 1 Corinthians 6:20.