This research investigates the development and validation of state-of-the-art high-fidelity m odels ofs oil cutting operations. The accurate and efficient modeling of complex tool-soil interactions is an open problem in the literature. Modeling options that provide more flexibility in trading off accuracy and computational efficiency than current state-ofthe-art continuum or discrete element methods are sought. In this work, two modern numerical methods, the material point method (MPM) and a hybrid approach, are presented with thegoal to simulateexcavation maneuvers efficientlyand with high accuracy. MPM, as an accurate, continuum-based and meshfree method, uses a constitutive model (here, nonlocal granular fluidity model) for computing internal forces to update particle velocities and positions. The hybrid approach, a combination of particle and grid-based methods, avoids explicit integration scheme difficulties and unnecessary computations in the static regime. Visual and quantitative data, including forces on the excavation tool, are collected experimentally to evaluate these two simulation methods with respect to geometry of the soil deformation as well as interaction forces, both as a function of time.