HC Kimball offers a unique approach and one I haven't tried.
In the two or so mirror I have removed......
The first one I worked an old handsaw behind the mirror, sawing away the spot adhesive (actually, it wound up being the paper on the drywall)....but I could only get 24" into the mirror. Subsequent prying led to the mirror breaking into a million little pieces!
The second mirror I was only indirectly involved with (my brother actually did the work). He got about 6 or so plumber's helpers (those red rubber toilet plungers) and using just water to seal the rubber to the mirror, placed them equidistant around the mirror then had 6 guys pull out at once. Slowly, the mirror came off.....but they sure looked funny doing it! (I was in another room watching and laughing :-) But seriously, if you try this, cover all body parts (including gloves) and use eye protection.