Mountains Animal Sanctuary Trust was ordered to pay £6000 after pleading guilty to a health and safety offence at Forfar Sheriff Court.
The court heard that on the day of the incident the volunteer had been using the bench saw to cut up pieces of wood from an animal shelter that had blown down.
The bench saw was defective and was missing a top guard and a riving knife, which holds the wood in place. However, there were a number of nails in the wood and the piece he was working on jumped when he pressed down on it. The volunteer's hand slipped into the rotating blade, which struck his thumb and forefinger.
Mountains Animal Sanctuary Trust admitted failing to carry put a risk assessment in or give any formal instruction or safety training to volunteers who used the bench saw.
Gary Aitken, head of Crown Office's Health and Safety Division, said: "Hopefully today's outcome will make it clear that organisations need to understand the implications of failing to carry out their duties as employers."