This is obviously a Christian perspective, but the ancient gods were demonic entities seeking the destruction of their followers. We see this in the worship of Molech, in which babies were burned to death in the arms of the idol, and in 1 Kings 18 where the prophets of Baal cut themselves to call down their god. As a side note, Planned Parenthood follows in these satanic practices by killing babies and chemically castrating children.

Leviticus 19:28 connects cutting oneself with tattoos, reinforcing the intuition that the permanence of a tattoo, even if not physically damaging, is a form of self-mutilation, and that it was a common practice at the time.

Many other religious traditions associate tattoos with religious practice, including the Egyptians Picts, Maori, Celts, Native Americans, Greeks, and modern Wiccans. So even if tattoos aren't necessarily self-mutilation, they're almost certainly a religious symbol.

Moderns like to dissociate one thing from another because we don't believe in a created order. But if there's such a thing as symbolic meaning, these different things can't be disentangled so easily. While most modern tattoos seem innocuous, it's also very common for people to get a tattoo when they experience a loss, or struggle with depression or suicidal thoughts, almost as if a permanent physical image has metaphysical implications.