Beavers are known for their gnawing performance, e.g., felling trees. Even though this is well known, the biomechanics of it are not, and so this is the focus of this study. The lower incisors work as main cutting tools so that their technical parameters were studied. There are 3 angles (adding to 90°) of importance in cutting: 1) the wedge angle, the angle of the incisor tip; 2) the clearance angle between tooth and material (tree trunk); and 3) the chip angle between incisor tip and the perpendicular to the surface of the trunk. Cutting is usually oblique to the wood fibers. For technical wood cutting tools, an optimal wedge angle of 27° is known under certain conditions, and for the incisor of Castor fiber the wedge angle was determined using micro-Computed Tomography (µCT) scans to be 26.95°. Potential cutting forces of beavers were estimated for wood chips (2 mm in thickness) of 3 sample tree species. For plum trees hardness forces ranged from 246 to 328 N, and for maples from 190 to 254 N. Finite element analyses were performed to determine stresses in the incisor under different loads on the incisor tip. Three hypotheses concerning gnawing were posed and are supported by the data: 1) The shape of the cutting blade of the incisor determines the geometry of wood chips and ultimately the maximum wood hardness that can be cut. 2) Clearance angle and maximum gape determine the maximum diameter of a tree that can be cut (if rough bark is neglected). 3) Functionally most importantly the lower incisors are optimized in shape and supporting tissue for compression stress with all forces being transmitted along the locations of the center of gravity in theoretical cross sections within the tooth, so that only compression occurs under load.