The justification of the correctness of the selected regimes for silicate glass, leucosapphire, and diamondite sawing based on the finite element modeling of friction node deformation is given. The natural oscillation frequencies for the shaft with the saw disk and the forms of stability loss are observed. The analysis of the temperature fields recorded during the sawing process is performed for the hardest sample (diamond). The nature of destruction for the side surfaces of the sawn pieces is analyzed.