I suggest the following to get the glass out of the housing:
1. Remove mirror with motor from housing (three screws hold motor). You will need to angle the mirror by hand into different positions (pushing on face of mirror) to get enough clearance to get a screwdriver on the three screws between the edge of the mirror and the housing.
2. Use a light lube oil (like zoom spout or sewing machine oil) on the motor gimbal where the plastic mirror backer snaps on.
Very gently and slowly pry the plastic backer panel off the gimbal It is easy to break it off the motor, I have done so myself.
Do not attempt to do this without lubing the gimbal thoroughly first, it will break!There are two drive rods, horizontal and vertical control, that insert into openings in the front of the mirror motor. These just slide out once the backer is snapped off the gimbal. Now the mirror panel itself is free, and if the glass needs to be removed for replacement it is much easier to do so without damage to the motor or the housing.
If any of the motor mounting tabs are broken (frequently the case) then effect proper repairs with epoxy and wire loops so the mirror can be solidly mounted back in the housing. The standoffs in the housing are also frequently split and don't hold the screws tightly. Repair these as well with a suitable epoxy (JB Weld works well if you degloss the plastic first with some sandpaper). Allow to cure fully before attempting to reassemble.
Often the three motor mounting screws are badly rusted. If you have a good hardware store that sells bulk hardware by the piece get some proper replacements as needed. I usually reinstall the mirror panel on the motor (snap it over the gimbal after lining up the two drive rods) then reassemble into the housing by angling the mirror enough to get the three screws in. It is exceedingly difficult to snap the mirror backer into the gimbal and keep the drive rods aligned when the motor is already secured into the housing.
One additional caveat for the driver's side mirror as it is heated; the heat element is two layers of copper foil with a resistive carbon film sandwiched between them. It is very easy to ruin by tearing the outer layer if you are removing the glass from the backer. I've found a heat gun (or large hair dryer at least) does well at softening the adhesive used by the factory (if glass has been reattached with RTV or VHB tape, all bets are off) so the glass can be pulled away (SLOWLY) from the heat element without destroying it. Careful prying it as well, any tool with a sharp edge can easily ruin the heat element as well. A plastic tapered pry tool is about the best that can be done, if needed.
I am not aware of any replacement heat elements that will fit this application, and I have looked extensively. Most current mirror heat elements are Mylar film with a resistive grid printed on it, and cannot be cut to size as it will ruin the continuity of the heat element. Since all replacements I've found are too large, or the wrong shape, they cannot be used.