The concrete-granite combined body is a typical binary material in engineering, with mechanical response properties that differ from monomer under triaxial circumstances. Concrete monomer (CM), granite monomer (GM), and concrete-granite combination body (CGCB) were subjected to quasi-static compression tests under various confining pressures. To reveal the overall crack propagation and failure mechanism of the composite specimens, SEM was used to study the fracture and interface microstructure of CGCB, and RFPA was employed to simulate the failure process of CGCB. Finally, based on the Mohr-Coulomb strength criterion, a prediction model for composite triaxial compressive strength was developed. The results show that the uniaxial (triaxial) compressive strength of CGCB is affected by the material size effect and the interface constraint effect, and the failure condition of the combined body shifts from uniaxial "Y" splitting failure to shear failure of the concrete component when confining pressure is increased. Under various confining pressures, the concrete away from the contact and the granite near the interface are damaged in turn, and shear fractures occur progressively, resulting in the splitting failure of granite components, according to the numerical simulation findings. The strength prediction model can match experimental data and numerical simulations effectively, demonstrating the accuracy of the model. The findings of the study might serve as a scientific foundation for the excavation and support of deep subterranean engineering constructions.