If your mirror is glued to the wall, the glue won't be easy to remove. To support a heavy mirror and prevent it from suddenly falling, builders usually use mastic or construction adhesive. There's always a chance the mirror will break during the removal process, so wear protective gloves and goggles. If the mirror is large, you also need someone to help you support the mirror when you work it loose.
Cover the mirror with packing tape to prevent glass shards from falling if the mirror shatters. Put on protective gloves and goggles.
Work a wood shim behind the bottom edge of the mirror and lightly tap it with a hammer to separate the mirror from the wall. When the gap is wide enough, slip in a pry bar and insert another shim behind the pry bar to anchor it. This shim prevents the pry bay from damaging the wall.
Pry the mirror away from the wall slowly and carefully. Move the pry bar and the shim on which it's resting back and forth along the bottom edge to release the entire edge.
Tap the shims along the sides of the mirror while you pull out the bottom. If the mirror is large, this is a two-person job. You'll probably hear drywall paper ripping during this procedure, but drywall isn't difficult to repair.
Angle the bottom edge of the mirror toward you to release the glue holding the upper part. Hold the mirror securely as the last of the glue releases to prevent the mirror from falling.