Abstract: This paper advocates a method for real-time physical deformation and arbitrary cutting simulation of heterogeneous objects with multi-material distribution, whose originality centers on the tight coupling of domain-specific finite element method (FEM) and material distance-aware meshless approach in a CUDA-centric parallel simulation framework. We employ hierarchical hexahedron serving as basic building blocks for accurate material-aware FEM simulation. Meanwhile, local meshless systems are designed to support cross-FEM-domain coupling and material-sensitive propagation while respecting the regularity of finite elements. Directly benefiting from the structural regularity and uniformity of finite elements, our hybrid solution enables the local stiffness matrix pre-computation and dynamic assembling, adaptive topological updating and precise cutting reconstruction. Moreover, our mathematically-rigorous solver guarantees unconditional stableness. Experiments demonstrate the superiorities of our system.