Porcelain tiles have a glazed or unglazed surface that you can file smooth with a handheld tile file. There are two basic versions of this tool. One is a small, grit-edged file with a plastic or rubber handle. A more basic version is a grit-covered piece of wire frame that is about 3 inches by 6 inches.
Place the tile right side up on a table, with the rough or damaged area hanging off the table edge by about an inch.
Place your palm on the undamaged edge of the tile facing you, and press down firmly. Point the file downward and at an angle to match the angle on the rough or damaged side of your tile.
Begin to file downward on the damaged area with smooth strokes. Continue filing until it's smooth. Gently file down and under the edge of the tile if you want it to have a bevelled look.
A tile vice can be used to hold your porcelain tiles.