Mounting a small mirror on frosted glass?
I would use a few dabs of silicone bathroom sealer at the corners and hold it in place until it sets. 

It wouldn’t take much to hold and if you want to remove it later dental floss slid behind acts like a chainsaw on the silicone. I glue plastic name plates to equipment at work, sometimes the instructions change so a new plate is needed, a minute and a couple feet of dental floss removes the old nameplate, your mirror would work the same.