This study analyzed the relevance of the fish cutting process and modeled the forces of useful and harmful resistances. The muscle tissue of fish was described by the Maxwell–Thomson rheological model. The process of cutting of tuna muscle tissue with a wire knife and a flat-back single-edged knife was experimentally researched. The obtained test results were compared with the results of theoretical calculations based on mathematical models. The quantitative dependence of the useful resistance force on the cutting speed was established, and the dependence of this force on the sharpness of the cutting tool was determined. The influence of temperature and measure of elasticity of the fish muscle tissue on the value of the useful resistance force was studied, while the dependence of the harmful resistance force on the movement speed of a flat-back knife was established. In addition, the influence of the thickness of a flat-back knife on the value of the harmful resistance force was investigated, and the effect of temperature and rheological characteristics of the fish muscle tissue on the value of the harmful resistance force was determined. Furthermore, the empirical dependences of the useful and harmful resistance forces on the process parameters were analyzed, and the values of the coefficients of the empirical equations and those of the coefficients of determination were calculated. The tests carried out confirmed the validity of the mathematical models and the assumptions made within the accuracy of the experimental data and the range of changes in the rheological characteristics of tuna.