The Material Point Method offers an alternative approach for simulations to, e.g., the well-known Finite-Element-Method. In there, bodies are discretized using so-called material points while the solution of the equations of interest is carried out on a computational background grid, see [1]. Three main steps are necessary for the simulation process during one time step, see also [2]. At first, the properties of the material points are mapped onto the grid nodes. After the accumulation, the solution is calculated directly on the grid nodes and then mapped back to the material points, followed by a position, velocity, stress and deformation update for each material point individually. For the next time step, the old grid is discarded and replaced by a new one since it does not carry any persistent information. This enables the material points to move independently of the background grid, avoiding mesh distortion at huge deformations as they may occur in, e.g., FEM simulations. In this contribution, three-dimensional metal cutting processes in vertical and horizontal direction are presented. These simulations incorporate the Johnson-Cook material law, see [3], that takes plastic strain rates as well as heat generated from plastic deformations into account. In this context, the grid-shift method is applied in order to achieve smoother solutions as suggested in [4]. References: [1] D. Sulsky, Z. Chen, and H.L. Schreyer. A particle method for history-dependent materials. Computer Methods in Applied Mechanics and Engineering, 118(1-2):179-196, 1994. [2] S.F. Maassen, R. Niekamp, J.A. Bergmann, F. P ̈ohl, J. Schröder, and P. Wiederkehr. Modeling of the Split-Hopkinson-Pressure-Bar experiment with the explicit material point method. Computational Particle Mechanics, 9:153-166, 2022. [3] G.R. Johnson and W.H. Cook. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Proceedings of the 7th International Symposium on Ballistics, 21:(541-547), 1983. [4] S. Maassen. The Material Point Method for dynamic Metal Processsing. PhD thesis, University of Duisburg-Essen, 2023.