Soak a paper towel in mineral oil. Rub the paper towel back and forth over the scratch using medium pressure. Oiling stone tile is often enough to remove light scratches from the surface.
Place a piece of 100-grit sandpaper on a hand sander and rub the scratch out. Apply mineral oil with a paper towel after the sanding is complete.
Buff small scratches out with a dry steel wool pad. Rub the steel wool over the surface to remove the scratches.
Wet down the tile and look for the scratch. If the scratch isn't visible when the tile is wet, use a color enhancer designed for stone tile to hide the scratch.