Mounting slate tiles to any surface requires the use of a substantial layer of mortar to hold the heavy stone in place and grout to fill the joints between tiles. During the tile installation process, the mortar can sometimes smudge the surface of the tiles. If not removed immediately, it will dry in small crags and crevices. Once it's dried in place, the hardened mortar mars the look of the tile, creating a dull patina that appears dirty and stained. Removing the mortar can be a difficult process, but it's not impossible. Even if you've sealed the dried mortar in place, you can remove it, though the longer it's been in place the more labor is necessary. Once removed, a few finishing touches to the tile create the look you intended upon initial installation.
Remove any sealant from the tile's surface if applied after the mortar dried onto the slate. Use a water soluble sealer remover purchased at a home improvement store. Apply the remover to the sealed surface of the tile with a sponge and wait about three minutes for the remover to break down the sealant material. Wipe the dissolved sealer from the tile with a rag.
Rinse the tile's surface with water to remove the sealer remover, and allow the tile to dry for about an hour before continuing.
Mix a 50/50 solution of vinegar and water and apply it to the dried mortar on the tile. Allow the mixture to sit for about four minutes to soak into the mortar.
Scrub the mortar on the tile with a stiff bristled nylon brush. Use firm back and forth motions with the brush to break up the mortar. Rinse the tiles clean after scrubbing and examine the surface for any remnants of the mortar.
Repeat the cleaning process, applying the vinegar and water solution each time, until you've removed all traces of the mortar.
Use stone cleaner solution and a stiff brass brush instead of the vinegar solution with the nylon brush if the mortar appears impossible to remove. This method is harsher on the tile, so take care not to scratch through the mortar into the tile itself. Repeat the cleaner application as necessary.
Seal the cleared tile by brushing a layer of tile sealant specially formulated for slate onto the tiles. The sealant will help to protect the tile from damage or wear.