To remove scratches from a mirror, start by cleaning the surface with a gentle glass cleaner and a soft cloth to remove any dirt or debris. Next, apply a small amount of metal polish or cerium oxide to the scratched area, using a soft cloth or cotton ball. Gently rub the polish into the scratch in a circular motion, being careful not to apply too much pressure. Continue buffing until the scratch becomes less noticeable or disappears entirely. Finally, wipe away any excess polish and clean the mirror with glass cleaner to reveal a smooth, scratch-free surface. Keep in mind that deep scratches may require professional repair or replacement.