*EDIT* Dumbass me didn't realize that this was 2000+. Sorry for not reading. If you have a 92-99 then read on. If not, please disregard.
You need to take the door panel off first. Once that is off you'll probably see a small plastic water deflector inside the door towards the front. Remove that too. Now you should have access to the 10mm nuts that secure the mirror. If I remember correctly, I used a 1/4" ratchet and socket for one and a 10mm wrench for the other. Have someone else hold the mirror while removing the last nut if your arms aren't long enough to reach around. You don't want the studs to scratch the paint of the door.