A mirror is made from glass with a reflective coating applied to the back. Use the same techniques for drilling a mirror as with drilling glass, but take care not to overheat the mirror or cause any damage to the reflective coating on the back of the mirror. Diamond-tipped drill bits should be used when drilling glass, as carbide-tipped bits tend to grab and take chunks out of the glass, leading to cracks and chips in the glass.
Place the mirror onto a work table, with a scrap piece of plywood underneath the area to receive the hole. Make sure that the rest of the mirror is properly supported so that the mirror isn't subject to any undue stress or flexing while being drilled.
Insert a diamond-tipped drill bit into the cordless drill's chuck and tighten the chuck. Set the drill's direction lever to forward with the drill's speed set on low.
Locate the spot for the hole and place a few drops of mineral oil on this spot.
Place the tip of the drill bit onto the spot for the hole and align the drill so that the bit is perpendicular to the glass. Start drilling slowly with very little downward pressure.
Squeeze the trigger a little more to increase the speed once the hole is started. Avoid using too much pressure. Allow the drill bit to do all of the work. Add more mineral oil occasionally to keep the bit cool and lubricated.
Drill until the bit has gone through the glass and into the plywood, then back the bit out of the hole. Clean up the excess mineral oil with a cotton cloth.
When drilling glass, be sure to wear protective eyewear.