With a "hollow door fastener", of course. Actually they used to say that on the package, but now they are just called "anchors". I remember when they went by the name "molly bolts".
For these fasteners, you drill a moderate sized hole in the door, then insert the fastener. You push its teeth into the door so it will not spin. Then you tighten the screw. On the back side of the panel, inside the door, it opens up like a spider. Then you pull out the screw, put on your mirror hardware, and drive the screw back in. There is a nut on the back of the "spider" that holds it into place quite solidly.
The only trick is that the non-collapsing part of the fastener -- what we call the "shoulder" -- must be the same thickness as the door. If the shoulder is too small for the thickness of the wall or door, the legs can't open. If it is too long, it will never cinch up tightly. You must match the shoulder to the thickness of the material you install it on, the thickness of the door panel itself. There are specifically labeled fasteners for the very thin panels of "hollow doors".