How can this mirror be mounted on a wall?
For a "floating" appearance you could use construction adhesive (or "mirror adhesive") to mount a board to the back of the mirror (just the central mirrored part), and use some form of hanger or French cleat to attach that to the wall, with the mirror itself out a bit from the wall. 

That would lend itself to wrapping that board with flexible light strip or rope lights to "halo" the mirror a bit and emphasize the stained glass edges by lighting behind them.