Stochastic simulation of post-failure landslide behavior in spatially variable soils is important for reliable hazard assessment, yet remains challenging due to geomaterial uncertainty and the high computational cost of high-fidelity methods such as the Material Point Method (MPM) [1]. This study introduces a Random Graph Network Simulator (RGNS) to accelerate probabilistic simulations of landslide post-failure processes in heterogeneous soils. The RGNS employs graph neural networks [2] to emulate MPM-based granular flow by learning local interaction laws among material points within a latent graph framework, enabling efficient, physics-consistent, and generalizable prediction of landslide runout dynamics. Trained on a limited set of MPM simulations incorporating spatially varying soil properties realized from Gaussian random fields (GRFs), the RGNS is validated across multiple slope geometries and GRF parameters beyond the training conditions. Results show that the RGNS accurately reproduces probabilistic distributions of key post-failure metrics, including runout distance, sliding volume, and influence distance, with coefficients of determination generally exceeding 0.93. Owing to its computational efficiency, the RGNS enables large-scale Monte Carlo simulations that would be prohibitive with conventional high-fidelity solvers. Application to exceedance-probability-based hazard zoning further indicates that deterministic analyses based on mean soil properties may substantially underestimate hazard extents in low-probability, high-consequence scenarios. Overall, the RGNS provides a practical and efficient framework for quantifying post-failure uncertainty in spatially variable soils, offering a promising avenue for accelerating probabilistic landslide hazard assessment and risk-informed decision-making.