I recently did this while the windshield was in the car, so it was a little more difficult. I looked at the solvent @ the FLAPS and found that it was nothing more than acetone. So, instead I bought a pint of the stuff (was on the shelf @ FLAPS).
I took a few drops of acetone and let it seep in around the edges of the mirror mount. Every few minutes, I put a little more on it and let it soak (on my windshield, some of it ran down the windshield and I had to be careful not to let it drip on the dash). I let it sit overnight and the next day it easily twisted right off with my hand. Just be patient, let it do its thing.
BTW, acetone is a great way to remove superglue. I use it routinely to remove glass that is superglued to a device at work. I just soak the whole thing overnight and the superglue is gone.
YMMV
Warrenoliver