Tried to glue mine from the outside. Could not hold parts together for the glue to hold. Did not last.
One way to repair.
Remove inner door panel. Search on a search engine "muth mirror install taurus" for instructions. PDF file is a Gen3 but similar enough.
http://www.muthco.com/techsupport/pdfs/21000540.pdf
Muth sells replacement custom mirrors. There could be some minor differences from your door.
Remove all screws. Should be about 8 most around the sides of the door, and some at the door handle.
Starting at the bottom. Pull or pry the inner door panel to pull out all plastic holders that grab in holes in the door. You will hear a ripping sound as the plastic comes out of the holes. Plastic holders are reusable.
Pull inner door panel up over the door lock plunger and the door handle.
Prop the door inner panel on blocks or something so that the wires do not pull too hard. It is not necessary to disconnect any wires yet.
Remove the speaker grille and speaker if any near the mirror. Mach type grill just pulls off by hand. Spkr has small bolts. See Muth instructions.
Do not need to disconnect wires yet so that the wire will keep the mirror from falling to the floor and breaking.
Unscrew the 3 nuts on 3 plastic spikes which is how the mirror holds on to the door. Spikes may be already broken. The mirror might just fall off and be held on by the wire. If the mirror is totally broken off, you should have a mirror with 3 plastic spikes and 3 broken fragments of plastic spikes.
Hold the mirror so it does not fall and unplug the round black connector from the mirror. This is the only wire you must disconnect. Remove mirror from car.
Before gluing the spikes together, find some small nails or screws that would fit inside the spikes to strengthen the joint. Cut off the nail heads and glue together the spikes with the reinforcing nails inside. I used cyanoacrylate gel. I do not know what the best glue is.
Reinstall mirror. Only one trick to reinstall inner door panel. There are 2 large plastic spikes in the inner door panel that fit into 2 holes in the steel part of the door. The spikes guide the inner door panel to the right place so the plastic holders will go the right way.
Buying a new mirror housing might be better but you might have to wait for delivery or go the junkyard route and you might have to remove the colored mirror cover and reuse on your new mirror housing.
Pic 1 Door. Pic 2 Door plastic holder, cables, plastic spike in inner door panel. Pic 3 Connector for Mirror.
Pic 4 Broken Mirror. Pic 5 Glued Mirror.