If money is in current circulation then take your paper money to your local bank. They will change the notes for fresh ones as they are required to change old or damaged currency and will return the offending notes to the central issuing bank. But if the currency is damaged quite badly you may have to jump through a few more hoops.
If you have a note that is in such condition that the value is questionable and special examination is required to determine its value, then you can claim via here (www.moneyfactory.gov/damagedcurrencyclaim.html).
If the amount the money isn’t worth it, you could try and spend it or pop it in your jeans and give it a cycle in the washing machine.
If the money is part of a collection, either antique or foreign currency and you specifically want to rescue that note then mold can be cleaned off paper money relatively easily. Mold thrives in damp and dark places, so you need to leave it somewhere dry and light.
Firstly isolate the moldy papers in a dry place away from other papers to which it can spread, and then separate each affected note. It is recommended that you do this somewhere very well ventilated, if not actually outdoors (as long as it isn’t too windy!).
Next, let your papers dry out, ideally in sunlight. When mold dries out it becomes powdery. This process shouldn’t take more than an hour. You may have to do both sides depending on the damage to the currency.
When the mold has fully dried you should be able to brush it off the paper. As the currency may be delicate, use a soft clean brush such as a toothbrush (use a new one rather than an old one which may still be damp and dirty) and gently sweep the dry mold off the paper onto some old newspaper.
Remember to wear rubber gloves while doing this task. You may also wish to employ safety glasses and a mask as to avoid inhaling spores of mold which can cause respiratory problems. Dispose of the newspaper carefully, ideally utilizing an outside trash can.