According to Tricia:
To float a decorative mirror directly on top of a mirrored wall, you do need to plan ahead. You should ask your contractor to add blocking to the area where the decorative mirror will hang. And when the mirror/glass vendor comes to measure for the wall mirror, tell them to cut out a +/-6” hole (depends on the size of your decorative piece) in the mirror so you’ll be able to attach hanging hardware.
If you live in an apartment, and don’t have this option, there is an alternative. Screw an I-hook in the ceiling very close to the wall above your vanity area. If need be, paint it to match the ceiling color. Attach a piece of fishing wire or any type of strong, translucent wire to the back of your mirror. String it through the eyehook and loop it back through the picture wire of the decorative mirror, so you don’t see any loose ends. Add felt bumpers to the back of your mirror if there aren’t any. The wire will be virtually invisible and the mirror should rest against the wall mirror.