Wearing gloves and protective eye wear, cover the mirror with packing tape, and remove any brackets on the outside edge of the mirror. Insert wooden shims into any small gaps between the mirror and wall. Tap the shims under the edge of mirror gently, and use a pry bar to pull the mirror away from the wall.
To safely use a pry bar, place the pry bar only on the shims, rather than directly on the mirror, and place a second shim between the wall and the pry bar to prevent damaging the wall. Work to release the top and sides of the mirror first, and support the mirror to prevent it from breaking when prying the bottom edge of the mirror away from the wall.
Another option is to heat the glue behind the mirror by holding a hair dryer at the corner of the mirror so the warm air blows behind the mirror to soften the glue holding the mirror in place. When the glue is soft, use a long putty knife to pry the mirror loose at the corner then use a windshield removal tool to saw the mirror loose. Repeat the removal process at each corner. After removing the mirror, apply primer and drywall patch to the wall to repair any damage.