Sheet metal forming processes are widely used in applications such as those in the automotive or aerospace industries. Among them, punching is of great interest due to its high productivity and low operating cost. However, it is necessary to optimize these processes and adjust their parameters, such as clearance, shear force or tool geometry, to obtain the best finishes and minimize crack generation. Thus, the main objective of this research work is to optimize the punching process to achieve parts that do not require subsequent processes, such as deburring, by controlling the properties of the starting materials and with the help of tools such as design of experiments and simulations. In the present study, tensile tests were performed on three steels with different compositions and three sample geometries. The information obtained from these tests has allowed us to determine the parameters of the Johnson–Cook damage criteria. Moreover, punching was performed on real parts and compared with simulations to analyze the percentage of burnish surface. The results obtained show that the methodology used was correct and that it can be extrapolated to other types of die-cutting processes by reducing the percentage of surface fractures and predicting the appearance of cracks. Furthermore, it was observed that clearance has a greater influence than processing speed, while the minimum percentage of the burnish area was observed for the minimum values of clearance.