The Roman word for tattoo was "stigma," and in modern times we use "stigma" to mean "a mark of disgrace and infamy."
This is no accident of history, as tattoos in Roman times were most often used to mark slaves and criminals. "Tax Paid" was often inked into the skin of slaves from Asia, and it was common for slaves to also have "Stop me, I'm a runaway" tattooed across their foreheads!
Given this, tattoo removal became a pressing need in the Roman Empire. Our friend Aetius, the Roman doctor who's detailed records have survived to this day, included a description for how to remove tattoos:
In cases where we wish to remove such tattoos, we must use the following preparations… There follow two prescriptions, one involving lime, gypsum and sodium carbonate, the other pepper, rue and honey. When applying first clean the tattoos with nitre, smear them with resin of terebinth, and bandage for five days. On the sixth prick the tattoos with a pin, sponge away the blood, and then spread a little salt on the pricks, then after an interval of stadioi (presumably the time taken to travel this distance), apply the aforesaid prescription and cover it with a linen bandage. Leave it on five days, and on the sixth smear on some of prescription with a feather. The tattoos are removed in twenty days, without great ulceration and without a scar." (Translated by C.P. Jones via Vanishingtattoo.com)
Another common tattoo removal technique was a poultice made from pigeon feces and vinegar that was to be left on the skin for an extended period of time. Let's be glad we've come up with some better ideas since then!