As a result of the worldwide population and welfare growth, the demand for energy (oil, gas and renewable sources) and raw materials increases. In the last decades, oil and gas are produced from more and more offshore sites and deeper waters. Besides energy, the demand for diverse metals and rare earth elements increases as well. These raw materials are often at the basis of new sustainable technologies e.g. permanent magnets for wind energy and battery packs for electric cars. The availability of these raw materials is essential for a stable development of the world economy. Unfortunately, for some of the crucial raw materials, the availability is sometimes very local and in various cases there is a monopoly forming. To reduce this economic risk, investments are needed to search and extract minerals from new locations. Large, metal-rich fields are found at the bottom of the sea, such as phosphate nodules, manganese nodules, cobalt-rich crusts and vulcanic sulphide deposits (often referred to as Seafloor Massive Sulphide, SMS). These deposits are mainly located in the deep sea, at depths ranging from several hundreds of meters to several kilometers. One of the technical challenges to enable production from these locations is the cutting or excavation process. Experiments have shown that the energy needed to excavate the material increases with water depth. Besides that, it is demonstrated that rock that fails brittle in atmospheric conditions can fail more or less in a plastic fashion when present in a high pressure environment, as would be the case at large water depths. The goal of this research is to identify the physics of the cutting process and to develop this into a model in which the effect of hydrostatic and pore pressures is included. The cutting of rock is initiated by pressing a tool into the rock. As a result, at the tip of the tool a high compressive pressure occurs, which leads to the formation of a crushed zone. Depending on the shape of the tool and the cutting depth, shear failures might emanate from the crushed zone, which will eventually expand as tensile fractures that can reach to the free rock surface. Through this process intact rock will be disintegrated to a granular medium. Additionally, the presence of water in the pores of and surrounding the rock influences the cutting process through drainage effects. The most relevant effects are weakening when compaction and hardening when dilation occurs in shearing and tension. Deformation of the rock causes the pore volume to change, resulting in a under or over pressure. As a result, the pore fluid needs to flow. The magnitude of the potential under pressure is limited through cavitation of the pore fluid, limiting further reduction of the pore pressure. The drainage effects cause the rock cutting process in a submerged environment to show a stronger dependency of both the hydrostatic pressure as well as the deformation rate. The numerical simulations are performed with a 2D DEM (Discrete Element Method). In DEM, the mechanical behavior of a rock is mimicked by gluing loose particles together with brittle bonds. Such a method shows strong resemblance with sedimentary rock. In order to include the effect of an ambient pressure as a result of the water depth and to include the presence of a fluid in the pores of the rock, a pore pressure diffusion equation is added to the model. The discontinuous results obtained with DEM are interpolated to a continuum field through the use of a SP-method (Smoothed Particles). Additionally, SP is used to solve the pore pressure diffusion equation. For that reason, the methodology used in this dissertation is referred to as DEM-SP. Thus far no direct coupling has been found between the input microscopic parameters, that define the properties of and interactions between the particles in DEM, and the resulting bulk properties of the particle assembly. For that reason, a sensitivity analysis is performed in which the effect of the micro-properties on the macroscopic behavior is investigated. Additionally it is proven that the addition of the pore pressure diffusion process to the DEM-SP model corresponds with the effective stress theory. It is also proven that when air is used as a medium in the pores, no significant changes compared to simulations without pore pressure coupling occur. Comparison of the numerical model with a set of tri-axial experiments on shale, in which the deformation rate is varied, shows that the model is well capable to describe both compaction weakening and dilatant hardening. In order to further validate DEM-SP, several experiments from literature are simulated. A comparison of 2D cutting experiments on tiles shows a good match for the chip size, chip shape and the required cutting force. DEM-SP is used to simulated drilling experiments on marble, in which the hydrostatic pressure is varied. These results show that the simulated behavior of the cutting process matches qualitatively with the experiments, i.e. the trend of increasing cutting force with increasing hydrostatic pressure. Furthermore a series of cutting experiments for the purpose of deep sea mining has been simulated. These results match both qualitatively and quantitatively. Additionally, both the experiments and simulations show the existence of a hyperbaric effect. This means that at a hydrostatic pressure which is significantly larger than the tensile strength of the rock the cutting process shear and cataclastic failure are more dominant, while at hydrostatic pressures significantly smaller than the tensile strength the cutting process is dominated by tensile failure and chipforming. Finally, DEM-SP is used to simulate the full cutting motion of a pick point on a rotating cutterhead, in order to investigate the applicability of the method to shallow water depths (<30 m) and to investigate the use of the method for the dredging practice. Even at shallow water depths the effect of an increased hydrostatic pressure shows significant differences. Furthermore, the simulations show a transition from cataclastic towards ductile cutting process based on the cutting depth. Additionally a transition between stick-slip friction of the cut material along the tool is observed, which is an indication for different wear processes. It is proven that DEM-SP is capable of solving drainage related effects in deformation of saturated rock. A range of rock cutting experiments are simulated and the results match well both qualitatively and quantitatively with respect to cutting force and hydrostatic pressure. Further improvement of the model can be achieved by extending the model towards 3D.