For hanging, I like to use 3M command stickers with a French cleat kind of setup. No damage to the wall or artwork. Applied to a clean surface they are quite strong.
With two small cleats on the back, and the “wall side” of the stickers peeled, just push the mirror on the wall, then lift off the mirror and put good pressure on the wall pieces of the cleats to ensure adhesion. Hang mirror back and done.
I use two pieces of medium (1/8") scrap glued together to form half of a cleat. This suspends the piece off the wall slightly, and is aesthetically pleasing.
To remove the cleats from the wall you just pull down the tab as directed and it will stretch and release without pulling any paint. I love those things. We use them for hanging 5 lb. Christmas stockings, for hanging car keys and hanging shower brushes on the tile.