This work evaluates the possibility of identifying mechanical parameters, especially upper and lower yield points, by the analytical processing of specific elements of the topography of surfaces generated with abrasive waterjet technology. We developed a new system of equations, which are connected with each other in such a way that the result of a calculation is a comprehensive mathematical–physical model, which describes numerically as well as graphically the deformation process of material cutting using an abrasive waterjet. The results of our model have been successfully checked against those obtained by means of a tensile test. The main prospect for future applications of the method presented in this article concerns the identification of mechanical parameters associated with the prediction of material behavior. The findings of this study can contribute to a more detailed understanding of the relationships: material properties—tool properties—deformation properties.