I did this when someone offered me free mirrors for a karate school I was building.
Wear heavy gloves and two layers of clothing. I stood on a ladder so that my chest was even with the top of the mirror. Start at the top by prying away from the wall so the glass starts to flex and hold it with steady pressure when you feel it is starting to reach a snapping point. Hold it...hold it... Eventually, the mastic will pop (you will hear the subtle ripping that will signal you're making progress, a sound like peeling your sweaty leg off cheap vinyl seats)
You are tearing the top layer of drywall paper off of the gypsum. Pry and hold further until you feel the next level pop. Rinse and repeat. When you get close to the bottom, get ready to support the entire weight of the glass, because it will drop after the last mastic circle has let go, unless it is supported by a J channel.
I was left with (8) 4 x 7 full panels of mirror, broke none of them. There were globs of mastic stuck to the back, but I just reattached it with new mastic is separate spots. Now transporting them was an entirely different story!
All this goes out the window if you're not attached to drywall...