Hot to remove soap dish holder affixed to tile with morter

There's really no good way to do that. You're better off cutting out the piece of tile and replacing it.

Since you are probably worried about using a hammer and chisel to remove the grout, for fear of cracking surrounding tiles; try a 4 1/2" angle grinder fitted with a dry cut diamond blade. It will cut through the grout and can easily cut the soap tray into pieces for ease of removal. You can buy the angle grinder and diamond wheels from Harbor Freight Tools (made by slaves in China) very cheaply. I hope this helps.