This research investigates the development and validation of state-of-the-art high-fidelity models of soil cutting operations. The accurate and efficient modeling of complex toolsoil interactions is an open problem in the literature. Modeling options that provide more flexibility in trading off accuracy and computational efficiency than current state-of-theart continuum or discrete element methods are sought. In thiswork, two modern numerical methods including material point method (MPM), and a hybrid approach are presented with the goal to simulate excavation maneuvers efficiently and with high accuracy. MPM, as an accurate continuum mesh-less 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 a 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 the simulations with respect to geometry of the soil deformation as well as interaction forces, both as a function of time.