Shower soap dish holders do not last long. Metal-type holders tend to collect water and soap scum and rot out. Tile holders are often used as a handle and pulled off the wall. Removal and replacement of both types of broken dish holders are fairly common repairs as houses age. To remove the metal type holder simply cut away any caulk, find your screw holes and unscrew the fixture from wall. Replacement fixtures are available at most home stores. For porcelain or tile soap dish holders the process is a little more challenging.
Insert a wash cloth into your shower drain. Place a painters cloth over the entire surface of the shower floor or tub floor. You want to make sure that none of your debris goes into the drain as it can solidify in your pipes causing a serious plumbing problem.
Get down beneath the soap dish and look upward. If you see a retrofit mounting plate, an opening in the porcelain and slots, then your soap dish was placed onto the wall after the tile was installed, which usually means it was replaced before.
Cut any caulk around the edges of the soap dish with a utility knife. Wearing gloves and goggles hold the remains of the soap dish in one hand. Using a rubber mallet, tap upward on the bottom of the soap dish. The dish should slide upward and come away from the tile wall.
Cut the grout around the tile-type soap dish using a grout saw. Try to stay in the middle of the grout. Use a small chisel to remove broken pieces of tile. It is sometimes a good idea to cover adjacent tiles with painter's tape to protect them during this process. Remove the tile by lifting it away from the good tiles. Clean up the underlying surface by slowly and carefully chiseling to remove excess adhesive or thin set.
Remove all of your broken tile and sharp pieces. Vacuum the wall where you want to replace the soap dish.