The original mirror stem is spring loaded (fed. safety), so if you grab it and slowly twist it 90 degrees, you expose the 2 mounting screws in the base. Some screws were screwed directly into the sheet metal, some were bolts into caged nuts, some were bolts with nuts on the inside of the door. With luck, you don't have to take off the door panel.
If it's not a loose base and the spring loaded stuff inside the mirror is loose, you'll need a parts mirror for little tiny parts to fix it.
Phil.