SDCL § 41-8-23: Killing of mink, muskrats, and beavers causing damage.

Mink may be killed at any time if doing damage around buildings but all such mink killed are the property of the state, if taken during the closed season. If muskrat or beaver are injuring irrigation ditches, dams, embankments, or public highways, or causing any other damage to property, the secretary of game, fish and parks may issue a permit to trap or kill such animals at any time. The Game, Fish and Parks Commission may authorize the killing or trapping of beaver upon public lands and game preserves at any time the commission deems necessary.