How can I re-silver a black mark on a mirror?

Use toothpaste. One of the most common solutions for mirror scratches is by using regular toothpaste that you use to brush your teeth. This will work on light scratches on your mirror. Take note that you need to use the white paste form toothpaste and not the gel toothpaste. Place a dollop of toothpaste on the scratched area. Use your finger to massage the toothpaste on the scratched area with a circular motion. Afterwards, use soft cotton cloth to wipe off the toothpaste from the mirror. The scratch should disappear.Use cerium oxide. Many jewelers use cerium oxide to polish gemstones and precious stones. You can also use this to remove the scratches on your mirror. You can buy glass polishing kits from the hardware store. If you have plenty of mirrors or glass that you want to restore, you can invest in the kit. Just mix the cerium oxide powder with a bit of water until you form a pasty substance. Spread the paste on the scratched area on your mirror and use the buffer in the kit to work it on the scratch. Wipe off the paste to inspect the scratch. It may take a while to completely remove the scratch on your mirror but it can be done with a bit of hard work. You can purchase the kit "Glass Polishing Kit"on Amazon.Mustard and vinegar. Another solution to mirror scratches is a mixture of dry mustard and vinegar. This is convenient since you may already have these ingredients at home. Mix equal measurements of dry mustard and vinegar. Mix them well to form a paste. Afterwards, dab the mixture on the scratched area on your mirror. Allow the mixture to work on the scratch for a few minutes. Afterwards, use a clean and non-abrasive cloth to rub the solution on the mirror in a circular motion. Inspect if the scratch has disappeared.

Try scraping it with a razor blade or a plastic scrubby. Hopefully it will clean off. The black has to be on the surface, not in the glass. Good luck.