Mink kill domestic poultry by biting them through the skull or neck. This is their calling card. They are also known to attack ducks and rabbits. Mink do not gnaw or burrow, but they use burrows made by rats. Mink love to hunt and tend to kill more than they need. They will even neatly pile up the carcasses after a killing spree.
Strong wire mesh is the surest way to keep mink out of barns and coops. They can also be trapped and removed, but care should be taken with identification as they are easily confused with native water voles, a protected species. Live trapping is the only option, so non-target species can be safely released