Once you glue ceramic tile onto a wall, it's generally there to stay. So much so that removal of the tile often involves destruction of the tile in the process. When you only want to remove a portion of the tile though, there is a way of doing so without damaging the tile entirely. Cutting through the tile with an angle grinder or rotary tool allows you to separate the unwanted portion of the tile from the wanted portion. This allows you to remove only a section of the tile, leaving the rest installed and intact.
Cover any doors of the room leading to other areas of the house with a sheet of plastic taped into place with masking tape to avoid dust from the cutting process spreading throughout the house. Cover any vents in the room with the plastic sheeting as well for the same reasons. Open any windows to provide ventilation and place a fan in the window directing air outward, to increase the air flow. Put on a pair of safety goggles to protect your eyes from ceramic chips and put on a respirator to prevent the inhalation of dust.
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Mark the cutline that you'll be making onto the tile face with a grease pencil. Place masking tape onto the tile running along the edge of the marked line over the tile piece that you wish to keep attached. The tape will prevent chipping on the tile that you aren't wanting to cut away.
Spray the tile surface with water placed in a handheld sprayer to keep the dust created from cutting down and to provide lubrication for the cutting blade.
Cut through the tile using an angle grinder. Start at one end of the cut line and run the blade along the tile surface to the other end. Spray water onto the tile when needed to keep the surface wet. Make multiple passes with the blade if needed, to cut through the tile and to the subsurface. Switch to a rotary tool with a tile cutting bit to cut tile closer to the edges of the wall where the grinder blade is too large to reach, or to make curved cuts in the tile. Do not wet the surface for the rotary tool.
Pry cut pieces from the surface with a small pry bar placed into the joints. Apply pressure to the bar as you move it behind the cut piece to pry it from the surface.
Remove any dust from the area with a vacuum. Then wash all surfaces with a water dampened rag to remove all traces of the dust. Keep the fan running in the window for several hours to help remove any dust remaining in the air after cutting.