Golfergal,
Going by your picture, I'd say the mounting neck itself broke free. I'm also betting there's another piece that broke. As stated by robby363, they design them this way so they won't injure someone or do more damage to the door if they are hit. The part that broke, from what I see is NOT replaceable, unless you can find a damaged assembly at a salvage yard, but most likely this is what will be broken on those too. Also, from your picture, it looks as though the shaft that pulled out had some sort of lock on it to keep the whole mirror in place, this may be the other 'part' that broke.
I was hoping I would have to say this, but...
I'd suggest getting a new mirror and having it installed at the dealer. It's worth it to have a new mirror assembly.
To be safe, ask the dealer if they have repair parts for the mirror assembly... I'm betting they don't.