Do a tattoer that uses letter and numbers actually cut through the ear or do they just use ink and permanently write it?

The clamp? Yes sometimes they go through the ear, ans sometimes it's better that way.

If you push hard you can punch through the ear which actually gives a better tattoo in my experience so I often do it on purpose. Although my clamp is old and lacks an ear release so sometimes the ear gets a bit stuck then which would be solved in 2seconds if the rabbit weren't thrashing and rolling in a ball because of it. Within a couple minutes that rabbit seems to have forgotten all about it though.

It's more like a puncture than a cut. It pierces a hole and the hole heals quickly.

I really need to get one with an ear release.