The bathroom mirror was attached to the wall with dry wall anchors. To make a long story much shorter, the mirror was yanked from the wall, dragging the anchors through the wall making large holes and a big mess.

I know, in principle, how to repair the holes, but I also know I can't hang the mirror in the same place after simply patching the dry wall holes.

Is my best bet to cut out the entire section of dry wall and then attach a horizontal(?) 2x4 or 1x2 to the existing drywall from behind, and then patch the hole with new drywall. I think I'd be able to then attach the mirror to my new 'stud'. I don't have any idea how I'd truly anchor my new 'stud' to the actual studs without cutting out a much larger section of the wall.

Thanks in advance.

I would cut out the drywall, from one stud to another, leaving the drywall covering half of each stud. It would then be easier to nail the new drywall piece to the studs. Before that, I agree with your idea of putting a 2x4 between the studs to hold your mirror. That 2x4 could be "toenailed" to the studs with a 3 inch screw or 2 1/2 in. screws. Good idea. It would hold better than putting drywall anchors in the new piece of drywall. I have done this myself in a living room, and it worked very well. Good luck.

Something you may want to try.

Something you may want to try.

Well aren't you sneaky. Great idea!