See step 7 above in hang a mirror using hooks for information on how to install drywall anchors and how to remove unwanted drywall anchors.
How to hang up a wall mirror.
Place a scrap piece of wood that is approximately half as long as the mirror is wide underneath the hanging wire on back of the frame.
Mark the location of the top edge and the center of the frame.
Find a place to hang the mirror.
Make sure you have enough space on the wall for the mirror and otherwise decide how you want it positioned relative to other items on the wall and in the room.
Finding a stud can be useful but not necessary if you have a strong enough hanger.
Lift the mirror into place and lock the two cleat hooks together.
Hold your mirror up to the wall to see how much space it will take up.
Hold the mirror against the wall at the desired position.
Gradually reduce your hold on the mirror until it is fully supported by the cleat.
Set the mirror down.