Soot and ash are messy agents that stain stone work. It forms around the edges of the chimney and hearth area after prolonged exposure. Soot is oily and sticks to stone like a slime in some cases, but it does clean up with persistence and the right tools. If you are trying to clean soot with water alone, it will make more of a mess. Approach the project with some basic planning and skill to make this clean up simpler.
Start a roaring fire in your fireplace by lighting kindling and piling on a few dry hardwood logs. When the fire is going well, throw two to three tablespoons of salt into the fire. This will loosen up those soot stains and they will go up the chimney.
Continue to use salt every time soot begins to accumulate on your stone work. This preventative maintenance makes cleaning simple and easier. Continue to clean the stone if soot builds up and continues to stain the hearth. Cleaning out the ash pit regularly will also help reduce staining inside the hearth and firebox area.