Shallow landslides pose a significant threat to people and infrastructure. Despite significant progress in the understanding of such phenomena, the evaluation of the size of the landslide release zone, a crucial input for risk assessment, still remains a challenge. While often modeled based on limit equilibrium analysis, finite or discrete elements, continuum particle-based approaches like the Material Point Method (MPM) have more recently been successful in modeling their full 3D elasto-plastic behavior. In this paper, we develop a depth-averaged Material Point Method (DAMPM) to efficiently simulate shallow landslides over complex topography based on both material properties and terrain characteristics. DAMPM is a rigorous mechanical framework which is an adaptation of MPM with classical shallow water assumptions, thus enabling large-deformation elasto-plastic modeling of landslides in a computationally efficient manner. The model is here demonstrated on the release of snow slab avalanches, a specific type of shallow landslides which release due to crack propagation within a weak layer buried below a cohesive slab. Here, the weak layer is considered as an external shear force acting at the base of an elastic-brittle slab. We verify our model against previous analytical calculations and numerical simulations of the classical snow fracture experiment known as Propagation Saw Test. Furthermore, large scale simulations are conducted to investigate cross-slope crack propagation and the complex interplay between weak layer dynamic failure and slab fracture. In addition, these simulations allow us to evaluate and discuss the shape and size of avalanche release zones over different topographies. Given the low computational cost compared to 3D MPM, we expect our work to have important operational applications in hazard assessment, in particular for the evaluation of release areas, a crucial input for geophysical mass flow models. Our approach can be easily adapted to simulate both the initiation and dynamics of various shallow landslides, debris and lava flows, glacier creep and calving.