The objection to self-mutilation is based on a natural law argument. It is intrinsically evil to harm the proper functioning of your body.
Now, it's pretty easy to see that amputating one of your fingers is disordered and impairs the proper functioning of your body. What about smoking three packs of cigarettes a day? That seems to impair the proper functioning of your body too. What about 1 pack? Once cigarette? There is something of a continuum here.
The same principle applies to tattoos and ear-piercing. Inasmuch as they increase your risk of developing an infection, they can be considered an evil, but they don't seem to impair proper body function. They're a marginal and borderline case.
The argument isn't based on Levitical law.