Cosmetic tattoos are a mortal sin because they are a form of mutilation, viz. intentionally and unnecessarily and permanently disfiguring a very beautiful and harmonious organ of the human body: the skin.
"Except when performed for strictly therapeutic medical reasons, directly intended amputations, mutilations, and sterilizations performed on innocent persons are against the moral law." Catechism of the Catholic Church, 2297
Recall what Blessed Pope Paul VI said in his prophetic encyclical Humanae Vitae on human love and life: "In fact, man does not have unlimited dominion over his body in general...of which God is the principle." HV. 13.
P.S. We might imagine some parts of the world where there is tribal warfare in which tattoos or some sort of branding of the skin is convenient and perhaps practically necessary for survival. In some specific case the mutilation involved in the tattooing perhaps may be considered necessary. However, often it seems quite out of place and wrong, even in many of those cases.
