Mounting heavy mirror that has a angled beveled frame
I would use a standard picture wire technique. Either one span for two wall anchors, or if that would show above the frame, use two shorter ones.
Purchase a frame hanging kit, which would include the screw-on eyelets, or just put screws into the frame and wire to those. You might have to experiment a bit to find out how much slack is needed in the wire.

Photo and more info from Home Depot
If you find that the frame vibrates against the wall when doors are closed, etc., a few felt pads would help.