Scrape the paint off the wall with a 5-in-1 putty knife. Hold the blade of the tool flat against the wall with the handle at a 30-degree angle to the structure to pry the paint off the brick. Hold the point of the tool against the wall to dig into grooves.
Pour mineral spirits into a plastic bucket. Dip your wire brush into the mineral spirits, and scrub the wall to remove any stubborn spots of paint. This procedure also removes deeper stains in the brick.
Let the mineral spirits soak into the wall for 10 minutes. Reapply mineral spirits with your wire brush to completely remove any paint spots on the brick wall.
Wait for 10 minutes to allow the mineral spirits time to absorb into the brick. Rinse the wall with a pressure washer to remove any remaining stains and residue from the mineral spirits.
Inspect the wall after it dries completely. Clean it again as necessary to remove all the paint.