Remove the surface dirt and debris from the exterior brick wall with a water hose. Begin at the bottom of the wall and move the water hose in a steady back-and-forth motion while moving upward.
Mix together 1 gallon of warm water with 1 cup of TSP. TSP, or trisodium phosphate, is a heavy-duty cleaner that is available at local home improvement stores. TSP will clean the exterior brick wall while killing mold and mildew. Wear a pair of rubber gloves when working with chemicals to prevent skin irritation.
Saturate a stiff scrub brush or stiff-bristled broom with the TSP solution. Work on only a small section of the exterior brick wall at a time. Begin at the bottom and scrub the brick wall with the saturated brush. Continue in this manner until you have cleaned the entire brick wall.
Rinse the wall with your water hose. Begin at the bottom of the wall and move the water hose in a steady back-and-forth motion while moving upward.
Alternately, clean the exterior brick wall with a solution of 1 gallon warm water mixed with 1 cup of ammonia.