1. Theoretical analysis of oscillations during cutting of rocks detected the presence of three maxima in the oscillation spectrum (located in the ranges 102, 103, and 104 Hz respectively for typical cutting conditions). The first two maxima relate to inertia-free relaxation oscillations of the stick-slip type, occurring as a result of projection separation and rock microinhomogeneity; the oscillation frequencies corresponding to them are of the order v/h and v/d (v and h are cutting rate and depth; d is grain size). 2. The Г-integral is invariant with cutting in a brittle regime, but under conditions of considerable plastic deformation it appeared to be a very effective tool since it made it possible to establish the main characteristic of cutting resistance (KIIc or Гc), to calculate the maximum cutting resistance Tmax, or to determine the cutter efficiency index.