Our bodies are temples. Temples that God created himself.  
Just like with a temple building, you would never mark it, graffiti it, or drill holes into it. The same is with your body. You should never mark your body or put holes into your body. 
I have a friend who is an evangelist and she decided to get a tattoo on the small of her back with a cross and a Psalms scripture on it. She tried to explain to me that it was acceptable to have a tattoo if it expressed your belief and devotion to God. I then explained to her that “Man looketh on the appearance, but God looketh upon the heart.” He knows if you are devoted to Him or not, through your faith, your words, and actions. I am not sure if she took to heart what I said to her but, I still stand by what I said. 
Not to mention, think about what your body would look like when you’re 50+? 
A lot (not all) of tattoos or piercings are also caused by a phase in life. So what if you finally decided to get it removed? All the money and pain to get it removed! 
Our bodies are more of a privilege sent from God, so in reality, our bodies are not essentially "ours." What we do with our bodies is under the order of Him, not only with tattoos or piercings, but with what we take into our bodies (Word of Wisdom), what comes out of our body (clean language), and relations that are saved only for marriage in order to multiply and replenish the earth. 
 
I hope this has helped and brought some consideration. 
Thanks! 
:)