Pour 5 ounces pine disinfectant cleaner into a bucket and add 1 gallon hot water. Put rubber gloves on and stir the cleaning solution with your hands.
Soak a scrub brush in the pine cleaner solution and scrub your outdoor wood table. Move the table onto the grass or another area away from other furniture so mold spores don't land on the surrounding furniture. Rinse your scrub brush, frequently, then reapply more pine cleaner and continue to scrub the black mold off the furniture.
Rinse your outdoor wood table with water from the hose.
Mix a solution of 1 cup bleach and 1 gallon hot water in the bucket. Apply the diluted bleach solution to your wood table using the scrub brush. Scrub the entire surface of the table to ensure the bleach kills any tiny mold spores that still remain after washing the wood with the disinfectant cleaner.
Hose down your wood table thoroughly to remove the diluted bleach solution. Pat your table dry with old, clean towels, then allow your table to finish drying in direct sunlight. Sunlight is also a natural mold killer and will rid your table of any black mold spores that still remain.