How can I get rid of mirror rot?

Mirror rot can be cut off or covered. It can’t be bleached off. You may have some success with a spray rust remover lubricant and a toothbrush. This will temporarily remove the black tarnish without helping the desilvering.

Most unframed mirrors are installed by gluing directly to the wall. Sometimes they can be removed in one piece and reused, but I wouldn’t count on it. It is very rare to end up with a usable mirror that was glued in. Mirror rot typically occurs along the edge so it can be cut off, but it requires removing it from the wall. Since the mirror will end up smaller, that may not be an acceptable solution.

Maybe you have a framed or vintage mirror with black spots you want to keep. Anywhere there are black spots you can assume the silvering was damaged at some point. You can restore the mirror, but don’t expect it to be perfect.

Start by removing the black tarnish. Make sure any chemicals you use are suitable for mirrors and won’t cause further damage to the silvering. The same goes for what you use to scrub. Don’t use foil, for example. Instead use something with soft bristles.  Reseal the area then use a silver paint or tape to cover it. Tape is a better option because it is less toxic and easier to replace if the tarnish returns. If it’s a small area with minor damage, it won’t be very noticeable. Be sure to avoid using adhesives on repaired areas.

Restored mirrors will be particularly susceptible to reoccurrences so keep them out of moist areas like bathrooms.

If you choose to cut the mirror or remove the tarnish, be sure to seal the mirror or it won't be long before it happens again.

Alternatively you can frame it to cover the edges. Beware though as framing may hold more moisture to the edges, exacerbating the problem.

Most people will find that the best solution is just to replace the mirror. No matter what you end up doing, take some steps to prevent mirror rot or all of your efforts will be for nought.