When a mirror needs restoration because of age or damage, it is not just the glass that is affected. A mirror needs proper support to ensure the glass stays protected, and a proper backing provides an aesthetically pleasing surface when the back is visible. A dried-out and cracked mirror likely needs the backing restored in addition to the glass for the mirror to look its best.
Apply multiple strips of masking tape across the mirror's front surface to prevent further fracture.
Undo any clasps that hold the back of the frame in place and remove the mirror carefully so you have access to the entire backing. If the mirror can't simply be lifted out, pry it out carefully with a putty knife or similar flat object.
Remove the paint on the backing with a plastic scraper to get the backing as clean as possible. Avoid using a vacuum when cleaning the backing because this could pull the backing off of the glass and damage the mirror's silvering even further.
Clean the backing further with a scrubbing sponge, warm water and a mild detergent. Use just enough water to dampen the sponge. Avoid stripping away the backing entirely; just remove any dirt or debris from its surface. Dry the backing gently with a towel.
Cover the mirror backing with epoxy.
Press a mirror of equal size and shape against the epoxy to create a new backing with the front glued to the back of the damaged mirror. Wipe away any excess epoxy that comes out of the sides as you press the mirrors together.
Place the mirror with the old face up to avoid further damaging the glass as it dries. If you place it face down, use a furniture pad to protect it.
Put the mirror back in its frame once the epoxy dries. It starts drying within minutes and is fully dry in several hours.