Reusing ceramic tiles is not recommended because they tend to crack or break during the removal process. However, reusing the tiles is possible if they remain intact. In order to reuse them, the substance used to adhere the tile to the floor or wall will also have to be removed.
Mortar is the compound commonly used to attach tile to another surface. After mortar has dried and set, it is hard to remove from the tile. A sander is able to even out the mortar but may not remove it completely from the tile.
Old mortar and new mortar do not set together properly. Starting from fresh, clean tile is the best bet for home projects.