Cover your mouth with a breathing mask. When dealing with moldy surfaces, always consider your health first and protect your airways. Mold can wreak havoc on an upper respiratory system, especially if you have mold allergies or asthma.
Remove the stucco. Moisture penetration usually indicates that the stucco has been compromised and will probably require replacement, so cut the stucco in small sections by running a circular saw along the surface. Cut the stucco in small squares and remove them one at a time. Do not make your squares extremely large, or they may prove too heavy to handle with ease. Try for a length and width of about 2 to 3 feet for each square.
Peel away the exposed stucco paper. In some cases, the paper may remain attached to the stucco itself, but any remaining paper should easily peel away. Wear rubber gloves to protect your skin from the mold spores.
Dispose of the paper carefully in an outdoor receptacle and move it as far away from your home as possible. Mold spreads very quickly, so use caution to contain the problem. If removing stucco paper from inside your home, place it directly into black trash bags and seal the bags tightly before walking the discarded material outside.
Dry the exposed wall material or framework. Since mold spreads quickly, you can safely bet that the spores have moved beyond the stucco paper and penetrated other areas as well, such as insulation or studs. If you now have direct sunlight hitting the exposed wall, you can allow it to dry on its own. Otherwise, use an electric heater or a dehumidifier.
Scrub any mold-affected framework using a dilute solution of 1 gallon water and 1/2 cup bleach. Replace any moldy insulation and cover the wall with new stucco or plaster board.