Remove passenger mirror on 1996 mustang covertable.

I have a 2003 Mustang, but assuming it is the same then check the following:

Do you have a speaker (tweater) in the door or just a plastic triangular cover (trim piece) on the inside of the door? If yes, open the door. The trim piece clips in place with plastic lugs. Lifting from the back edge the piece should rotate out either exposing the tweeter or the 3 bolts holding the mirror in place. If the tweeter is there, you will need to remove the speaker first. The bolts for the mirror are attached to plastic, so do not overtighter the nuts when reinstalling or you will have to buy a second mirror. Hope this helps.

If you do not have the triangular piece (i.e. door panel is one piece), the Chilton's manual says the door trim panel must be removed first.