What do I do if I spill oil on my asphalt? First you want to remove the oil as quickly as possible. If the oil is left on the asphalt it will soften the pavement and eventually destroy it leaving a hole and a stain. First things to do are: 1. Using a cloth wipe up the excess oil. 2. After cleaning up the excess oil. Apply speedy dry or kitty litter to the spill area. Move it around, back and forth using a broom. You are trying to have the kitty little or speedy dry soak up