Due to the insufficient accuracy of existing studies of frozen sedimentary rock cutting process for practical calculations, the article solves the problem of determining the tangential component cutting resistance for blocked, deep blocked and cell cutting, which are currently the most commonly used methods in earthmoving equipment. The cutting tool and rock mass force interaction is considered from the point of view of the emerging stresses, which act on the separated chip element. The analytical dependences for determining the tangential component of cutting resistance were obtained. The numerical explanation of the choice of cell cutting in relation to blocked and deeply blocked cutting is given. For all three methods of cutting, under equal geometrical parameters of the cutting tool and the physical and mechanical properties of the frozen rock, the numerical value of the tangential component of cutting resistance is obtained. The comparison of the cutting resistance estimated values has shown that cell cutting requires relatively less energy and is preferred during the process of frozen sedimentary rock excavation. During field and laboratory investigations with the use of a multi-purpose cutting stand, a sufficient convergence of the analytical statements with the physics of frozen sedimentary rock cutting process was established. The results of the research allow a more reasonable approach to the adjustment of existing methods for determining the required tractive force and power for the drive of an excavation machine, and, therefore, to the actual efficiency and profitability of work.