To remove mold without replacing the shingles, use a mixture of bleach, water and trisodium phosphate. Mixture amounts vary, but the most common formula is one part bleach to four parts water and a small amount of trisodium phosphate according the manufacturer's instructions.
Do not use a power washer, as this could damage the roof. Chlorine bleach can be harmful to plants, so you should protect your plants while cleaning the roof. After spraying the shingles with a pump sprayer, let them soak for up to 20 minutes. You can rinse off the mixture with a normal garden hose with clean water.