The best way to do trepanning is to make a fixture to hold the axle of the cutter. A large plywood pully will do very nicely for reducing the speed of a motor so that the torque is increased. A drill is basically not enough torque to do even a little 6" mirror.
You also want to add enough pressure so that the grains go crunchy very nicely and you probably should have a way to lift the cutter so that fresh grit can work it's way under the cutter.
You should be cutting at the rate of about 2" or so an hour with a decent pressure.