tape the mirror up and take all the safety precautions as Dodgeman stated. Then with a box knife, keep scoring the outer perimeter of the mirror on the drywall until the knife goes through the drywall all around. You will have the studs that you encounter, just go down to them. Now the mirrow will be held up on the drywall by the several nails holding the rock to the studs. Carefully wiggle the mirror and attached rock until the nails work through.
Now, remover the mirrow and the rock intact, leaving a nice square hole. lay the rock and mirror down on a new piece of rock and trace the both out on to the new rock. score and cut it. Then do any sistering of studs for nailing boards. attach and do the necessary taping and bed work. Then texture then prime then paint. Its done.
No glass breakage, the rock will be rendered damaged both ways since the outer skin will come off and show the gypsum. You can save some time and some blood and the rock is replaced and ready for texturing.