Spray with mold killer and try to bristle brush it off with vinegar, soap and water. If already soaked in and damaged the wood, may have to sand it down and stain
To spot clean mold, mildew or moss from a cedar fence, use the following technique:
Bleach will lighten the mold’s color but does not kill it, and the scrubbing might remove some, but “stubborn “ mold means you need a good product that specifically kills mold. I would use it after the bleach scrub and let it penetrate well. And then stain or paint the wood to protect from moisture to limit regrowth.
A power washer with the right liquid cleaner should work.
If you are a patient person, you could spray with Wet n Forget. It works slowly, but lasts a long time. You are going to need to look at the cause of the mold too, such as dense vegetation preventing ventilation.
My usuall "go to" for removing mold is bleach. in water. diluted so that I don't bleach out color. However, mold is killed with chlorine bleach like clorox.
I tried bleach. Mold comes back. Vinegar full strength kills it: two years and counting.