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Reusing old tiles is possible as long as the remains of mortar glue are removed from old tiles or old slabs. A chore that requires care and a lot of time.
The solution to make your job easier? Lay the tiles on the grill of an electric barbecue set on soft heat. The residues softly soften and can be easily removed with a spatula.
Perform a test beforehand on a single tile, just to verify that it supports this type of treatment without splitting.

Video Instruction: How Do I Remove Old Adhesive From Ceramic Tile?: Ceramic Tile Repair