Debris flows are highly nonlinear and transient geohazards characterized by complex interactions among rainfall triggering, sediment entrainment, multiphase flow evolution, and topographic constraints. Numerical models based on physical governing equations have significantly advanced the understanding of debris-flow dynamics; however, their high computational costs limit their application in real-time hazard prediction and rapid risk assessment. Developing efficient surrogate models capable of accurately reproducing dynamic processes remains a critical challenge for intelligent debris-flow early warning systems. This study proposes a deep learning-based spatiotemporal decoupled surrogate model for rapid prediction of debris-flow dynamic processes. The proposed framework introduces a novel spatiotemporal decomposition strategy, where the complex evolution of debris flows is separated into spatial feature representation and temporal dynamic reconstruction. A deep neural network is developed to learn the nonlinear mapping between controlling factors, including terrain characteristics, material properties, and initial flow conditions, and the corresponding flow evolution fields generated by high-fidelity numerical simulations. By decoupling spatial and temporal dependencies, the proposed model effectively captures the intrinsic patterns of debris-flow propagation while significantly reducing computational complexity. The performance of the surrogate model is evaluated using large-scale simulation datasets and validated against benchmark cases involving complex channel geometries and dynamic flow processes. Results demonstrate that the proposed model can accurately reproduce key dynamic characteristics, including flow velocity, depth evolution, and inundation extent, while achieving orders-of-magnitude acceleration compared with conventional numerical simulations. Furthermore, the model maintains strong generalization capability under different terrain conditions, providing a promising approach for near-real-time prediction of debris-flow evolution. The proposed deep learning surrogate modeling framework establishes a new pathway from physics-based simulation toward AI-driven dynamic prediction, offering a powerful tool for integrating numerical modeling, multi-source monitoring data, and intelligent early warning systems for debris-flow hazards.