Turn off the power and water to the backsplash. Remove any outlet covers from the wall with a screwdriver and set them aside. If the pot filler is fully installed, unscrew the escutcheon plate by locating the screw on the underside of the plate and twisting the filler to remove it from the wall, leaving behind only the pipe.
Lay out the backsplash tile on the counter, in front of the wall where it will be installed, to determine the best layout and where to place the cuts. Make marks on the tiles to be cut to fit around the outlets, edges of the installation and the pot filler with a pencil. Hold the individual tiles up to the outlets and pot filler and trace the outline of the hole onto the tile to determine where the cut should be made.
Make all necessary cuts on a tile wet saw. To cut a square notch in the side of a tile to fit around the pot filler, cut the two parallel marks on the tile with a wet saw. Use tile nippers to remove the inner portion between the two cuts.
Use a variable speed drill fitted with a hole saw and guiding bit attachment to make a hold in the center of the tile for the pot filler to go through. Place the guiding bit in the center of the area to be drilled and twist it slightly to help it bite. Drill slowly until the guiding bit is through and the hole saw is beginning to cut the hole in the tile. Drill more quickly until the hole saw has bored a hole through the tile.
Spread mortar directly onto the backsplash and beginning installing the tiles in the same layout you determined on the counter. When you get to the pot filler pipe, spread the mortar onto the back of the tile, rather than the wall around the pipe and press the tile into place around it.
Let the tiles dry for 24 hours, then grout the installation using a grout float to spread the grout. Hold the float at a 45 degree angle to spread the grout and at a 90 degree angle to scrape off excess grout from the tiles. Wait 10 minutes, then clean the tiles with a slightly dampened sponge.
Let the grout dry for 24 hours, then screw the pipe filler back on and reattach the plate. Reattach the outlet covers and turn on the power and water to the wall.