I'm not familiar with a 300, but I did same on my 94 320E with elec/heat.
1- Inside door panel has seperate trianglar trim - slide it UP to release.
2- Unplug wireing harness.
3- Remove 3 screws to release mirror from door.
4- Painted mirror bezel and surrounding spacer are compression fit with many interlocking tabs on 3 sides. You may be able to squeeze the bezel to release a few tabs on top or bottom and pull straight away to seperate. If not, use a very thin screw driver to pry the spacer away from the mirror housing.

Good luck and try not to scratch the paint.