What is causing a strange protrusion to come out of the wisdom tooth removal site?

Clot: You don't mention what the "protrusion" looks like or how long ago the tooth was extracted so i will offer some possibilities. If it is soft and looks like red/purple jelly then it is the blood clot that has protruded from the socket. If it is hard then it could be a bone spicule or a tooth root.

Excess bone: Sometimes excess bone works its way to the surface and is normal . Check with your dentist to make sure.