Scrape up any Royal Purple oil, grit or sand with a putty knife before sweeping the area clean. Apply an oil-specific cleanser to the area, and allow it to work into the oil according to the manufacturer's instructions. Remove the cleanser and repeat as necessary until the stain is gone.
After the area is free of grit or debris, apply a cleanser such as Pour-N-Restore to the stain, troweling it in a circle an inch wider than the diameter of the stain. Wait for the product to dry to a powdery texture, which can take as long as eight hours or more. For best results, use this product when temperatures are above 60 degrees Fahrenheit, or heat the environment to that temperature if the stain is in a garage or other indoor space. Sweep up the powder, discard it, and wait for the moisture to evaporate. Repeat the process if the stain is still present after the moisture has gone.
For smaller spots, environmentally safe products such as Griot's Oil & Grease Cleaner are effective. Follow the instructions on the label for diluting the cleanser, and spray it onto the spot. Allow the cleanser to set for up to five minutes, and spray it away with a hard blast from a hose.