Any ideas for repairing water damage on outside corner with a rusty corner bead?
I see no need to get into the tile here. I would just do a light scrape, then sand it down. Seal it with a stain-blocking primer, then do any drywall repair. Prime it again and paint.

Replacing part of the bead with plastic could help prevent further rust if you're unable to rectify the water issue. Surgically remove a section of the metal bead using a rotary tool and cutoff wheel. Cut and fit a section of plastic bead. I wouldn't rely on joint compound alone. It'll be too fragile.