How to I clean the paint out of copper pipe?
I have to presume that you really mean "off of the copper pipe".
Paint can be removed from the copper pipe using steel wool. A course style will be better to begin with and follow up with a finer style to nicely shine up the copper pipe.
If the paint is extra thick you could try removing a good bit of it first using a sharp utility knife to peel most of it off the pipe.
Jell type paint remover is another option to soften the old paint but that option comes with its own set of extra concerns with odor and caustic nature when handling it.
With any type of paint removal like this it is highly advisable to question the possibility as to whether the paint is a lead bearing type. If so you need to take proper precautions with respect to any dust and debris created as a part of the paint removal.