Whats the best way to drill this for hanging things like a mirror? Installing as an accent wall in a small bathroom over cement board.

Instead of drilling through the stone, you could attach a small piece of wood to a stud the same thickness as the stone panel,where you want to hand your mirror, and install the stone around the piece of wood. The wood could be painted a dark color and will be hidden by the mirror. This will give a more secure surface to attach the mirror hardware to and prevent from having to drill through the stone. if you would prefer to drill through the stone, you would need a diamond drill bit and drill through to the substrate underneath to insert an anchor to attach the mirror.