Cover the point on the tile where you wish to drill your hole with crossing pieces of duct tape. Place one piece of tape over the other to form an “X” on the tile with the drilling location positioned at the center of the “X.” The tape will prevent the tile from shattering or chipping as the drill bit proceeds through it.
Set the speed of the drill to between 100 and 200 rpm. Moisten the tape slightly with water from a spray bottle at the center of the “X” to prevent the bit from overheating.
Position the point of your drill bit onto the center of the “X.” Use a diamond or carbide-top drill bit for creating clean holes through most tile material.
Start the drill, holding the bit firmly in place against the surface of the tile to prevent its moving along the face of the duct tape. Push gently on the drill as you proceed through the tile until you break through to the subsurface beneath. Continue drilling until you’re through the subsurface as well. You should notice a sudden easing of pressure on the drill bit as you make your way through the subsurface due to entering the wall cavity. Spray the drill bit with water occasionally when drilling through stone tile to keep the bit lubricated and to avoid overheating.
Release the drill trigger, and wait for the bit to stop rotating before you ease the drill from the hole. Remove the duct tape to reveal the drilled hole through the backsplash and wall.