It is difficult to remove pray paint from a brick wall without damaging the masonry. Follow these steps to complete the task.
Be sure that the masonry you're trying to clean is real brick. It makes a difference in the products and methods you'll use.
Borrow or rent a heavy duty power washer, with at least 3000 psi pressure. Wear protective eyewear, rubber gloves and other items to protect your skin while using the power washer.
Try power washing the spray paint with a mild cleanser or a mixture of bleach and water. If the mild cleanser does not work try a more potent one.
Make sure the tip of the power washer isn't too narrow, otherwise you'll etch a permanent outline of the spray paint into the brick.
Keep moving the tip of the power washer around, being careful not to stay in one spot for too long which could damage the surface of the brick.
Try a stronger chemical, specifically made for spray paint and graffiti removal, if you still can't get the paint off. The Newhome website has a report, entitled "Graffiti Remover Research and Field Test Report: The Search for Safer Products" which names 35 different cleaners. Taginator finished on top of their list for cleaning brick.
Try using a sand blaster if the power washer isn't removing the spray paint.
Try harsher chemicals if regular cleansers and bleach don't work. Balance the safety of the chemicals with the need for getting your brick clean.
Use extreme caution in using harsh chemicals, which may damage you or the environment. Use in ventilated areas.