In computational fracture mechanics, the consistent application of fracture numerical methods and crack surface representation methods adopted in the simulation is a critical issue. Existing methods still have deficiencies in the characterization, evolution, and topological changes of complex non-planar cracks. Based on an effective numerical method, we proposed an effective crack propagation algorithm driven by explicit crack surface evolution, realizing the accurate simulation of planar cracks (Mode I and II) in 3D elements, as well as the characterization algorithm for arbitrary complex non-planar cracks. This achieves an effect similar to the eXtended/Generalized Finite Element Method (X/G-FEM), where the crack surface is completely independent of pre-defined computational elements before implementation. Subsequently, after the interaction between the crack surface and elements, the computational domain and the constructed explicit surface interact with each other, which is analogous to the remeshing Finite Element Method (remesh-FEM). We successfully integrated the geometric topological evolution advantages of a novel method, thereby stably realizing crack surface shrinkage, coalescence, branching, and non-planar topological evolution within a unified computational framework.