Work like a beaver is an expression used to describe someone who works hard and diligently. It is derived from the behavior of beavers, which are known for their industriousness. To work like a beaver means to GNAW and DAM, which are two activities that beavers are known for. Gnawing is the act of biting or chewing something persistently, while damming is the process of building a barrier across a river or stream to control the flow of water.