Feel for you mate. I would think you could replace the mirror assembly but may need to take the door apart to do it.

 

Looking at that picture i think the piece of metal left behind is part of the mirror and not part of the door. you will need to remove the door card and the trim on the inside of the door to get to the bolts that hold the remains of the mirror on.

Have a look through the threads about fitting door warning lights for pics and instructions on how to remove the door cards.

 

Sorry to hear about your damage, but I cant imagine how ugly the car would look with wing mirrors......

That's why vw mount them on the doors.

Apologies, just had to comment.