Place the blade of a chisel at a 45 degree angle with the mortar and tap the head of the chisel with a hammer to chip away any large chunks of mortar.
Scrub the surface of the limestone gently with a wire brush to dislodge most of the remaining small particles of the mortar. At this point, the limestone may still be stained, but if you rub your hand on it, it should feel smooth.
Fill a bucket with an acid-based cleaner, such as muriatic acid, available at a home improvement store. Add enough water to dilute the mixture to 5 percent acid solution.
Wet the limestone completely and then insert a scrubber brush into the acid mixture and apply it to the limestone in the areas that are still stained with mortar.
Allow the acid solution to sit for 5 to 10 minutes and then scrub the area vigorously with the scrub brush. Continue scrubbing until the mortar is completely removed.
Rinse the solution off with a garden hose to remove all traces of the acid.