The accurate numerical simulation of geophysical flows of granular materials remains a central challenge in computational geomechanics. On the one hand, this is due to the need for complex constitutive laws that capture key features of the material, in particular cohesion and rate-dependent behavior, which govern flow dynamics. On the other hand, it requires numerical schemes capable of handling large deformations and evolving flow regimes reliably. In this contribution, we show how cohesive (elasto-)viscoplastic rheologies, in the framework of Perzyna-type viscoplasticity, can be formulated and applied within the Material Point Method (MPM), focusing on pressure-dependent and rate-sensitive constitutive models that combine mu(I)-type and critical-state-inspired granular rheologies [1]. Using these models, we demonstrate the ability to capture cohesive flow behavior and reproduce key phenomena such as the transition to plug-like flow. In particular, velocity profiles of various cohesive rheologies will be discussed. Applications to snow avalanches and slushflows are presented, highlighting the role of cohesion and viscosity in controlling flow mobility. The presented results are demonstrated using the open-source~MPM software Matter [2], providing an efficient platform for modeling elasto-viscoplastic granular flows.