Use a glass cutter to run scores across the face of the mirror in a roughly plaid pattern. The idea is to give the mirror some encouragement to crack when you start to pull it off. Smaller pieces are good to handle. Do not run the glass cutter along the same score multiple times. One firm score is enough.
Make the scores no farther than 6 to 12 inches apart. Now, tape up the entire mirror. Packing tape would work, as would masking tape. Use enough tape to stop any pieces from falling down and shattering or hurting someone.
Now, use a hammer or pry bar to lever up under one corner of the mirror. As you pry out slowly, tap with a metal object (a small hammer is good, but anything will work, even a heavy screwdriver or the back end of the glasscutter) along the scores you made with the glass cutter. The glass will probably start to crack now along the score line you made. Break away the mirror in small pieces so that you can carry it away easily.
Be very careful of the edges, as they will be sharp. Wear good gloves as well as eye protection. When you are done, sweep up the area carefully, then vacuum. Make sure there are no slivers of glass on the floor.