Mix a non-ionic detergent in a bucket of water. Use the amount of detergent recommended by the product's label. Test the mixture on a small area of the stone wall. If no discoloration occurs, dip the brush in the mixture and scrub it gently over the graffiti.
Make a thick poultice using as much kaolin as is necessary to cover the graffiti. Mix it with just enough of an organic solvent cleaner to turn it into a thick paste. Apply the poultice to the graffiti and tape a sheet of plastic over it to prevent it from drying too quickly.
Apply a paint stripper that contains organic solvents to any remaining graffiti. Test the stripper first on a small area of the wall, then apply it according to the instructions on the brand's label. Use a hose to wash the area underneath the graffiti immediately so the stripper does not stain the wall below the graffiti area.
Use a pressure washer as a last option. Stand at least 3 feet away from the wall and set the pressure washer to the lowest setting. Apply the water in overlapping strokes.