Pretty sure electric mirrors are just driven from basic dc motors with a series of light duty plastic gears. Sounds like the motor is spinning, but the gears that drive the linkage to move the mirror are skipping.
Crack open your wing mirror and look for broken gear teeth, something jammed in the gears, or the drive motor shifting around from not being properly fixed in place. Any of these could cause the gears to skip, which would explain it clicking and not moving.