Too simple but it works
I know this sounds too easy but I have used it a 100 or so times and never had a problem. This is on raised head pull rivets like the LP series.
Just take an electric drill with a 7/16 drill bit and drill it out,.... whoa though,..
Actually, just drill fairly slowly with reasonable pressure. The bit is so much bigger than the rivet head that it looks like it is cutting almost flat. As you remove enough material that you think you will actually get through the head and into the underlying material, the head will catch and just spin off leaving no marks and the stem of the rivet. Just punch or pull it out.
I have never had a well set rivet spin using this method but if the rivet is loose, this won't work unless you can hold the rivet stem. If you have to do that, I like the small flush side cutters that you use to cut electrical wire. These will hold, cut, and pull.
It also helps if you have to punch out the stem to back it up on the shop head side. I use a piece of lead shaped like a solid tube about 3 inches long with a 1/4" hole about 1/2" deep drilled in the end. Put the shop head in the hole so that it backs up the material. That way, when you punch the rivet stem, it won't distort the material around the hole. One made of wood will work but the lead is so dense, it really works much better with more mass.
Hope any of that helps!