A convenient and efficient approach to simulate the excavation-induced rock fracturing process from continuity to discontinuity is proposed. The excavation boundary is considered to be an internal discontinuity, which is enriched by a Heaviside function. By using partition of unity concept and level set method, the cellular automaton updating rule for elasto-plastic fracturing induced by excavation is developed. The excavation induced rock mass strain localization is described by plasticity. A plastic strain-dependent criterion is proposed to link continuity and discontinuity, by which crack initiation and propagation of rock mass are described. By using the cellular automaton neighborhood information and level set method, the crack propagation path and excavation boundary can be tracked efficiently. The excavation and the induced crack initiation and propagation can be represented and simulated without explicit remeshing. This approach is implemented in a self-developed numerical model, i.e. a rock continuous-discontinuous cellular automaton (CDCA). The reliability and versatility of CDCA in the modeling of excavation-induced crack initiation, propagation, coalescence and block formation in rock mass are well demonstrated. The method helps estimate the onset of stable and unstable failure development, as well as the magnitude of plastic strain before cracking in rocks.