Wipe up any food particles or clumps of BBQ sauce that you see on the deck.
Apply a sodium percarbonate-based cleaner to a nylon brush. Sodium percarbonate, otherwise known as an oxygen bleach, is the type of cleaning solution that you want to use on a deck. While you might find deck cleaners that contain chlorine bleach, these cleaners can damage the deck's wood fibers during cleaning.
An oxygen-based bleach will remove common stains such as BBQ grease, in addition to mildew stains and the discoloration from UV degradation. Don't apply the solution directly to the wood. You want to only focus on the area of the deck that is stained, which is why you should apply the solution to the brush first.
Scrub the grease spot vigorously until a foam forms.
Rinse the area with a clean, wet towel or spray it away with a water hose. Clean again if necessary.
Wash the area with a power washer if the chemical cleaner does not remove the grease. You can rent a power washer from a hardware store. Don't put the setting too high for the first wash and be cautious that too much pressure could damage the deck wood.