I found a driver side heated mirror glass on RockAuto for my Avalanche.
It was not expensive, and it works great now.
The passenger side mirror does not defrost, but I haven't been too concerned about it - as the glass itself is not broken or cracked.
The glass will detach from the mirror motor assembly by prying on a bunch of tabs that are in a circle, using a thin screwdriver. Tilt the mirror glass all the way in as far as possible, and you will see the circle of tabs. Pry on them gently one at a time while pulling on the mirror glass and it will eventually detach enough to pop right off. Just be careful not to break the tabs on the motor housing. A little tricky to do, but not too bad. Then simply unplug the wires. Of course, check that the wires and connectors are not broken or damaged. Then, test the circuit, as BainMan has outlined.