The best way I've found to remove permanent marker off of glass and glass mirrors is to use an SOS pad.
Take an SOS pad and soak it in warm and soapy water and then use the abrasive portion of the SOS pad to scrub off the permanent marker.
You might have to scrub a few different times to get the permanent marker off the mirror but it always works for me.
Nail polish remover, WD-40 and even Rubbing Alcohol are some other good things to use to remove permanent marker from glass and mirrors.