The combined finite–discrete element method (FDEM) is an advanced numerical calculation method that is highly suitable for simulating the entire rock blasting process. Considering that rock mass contains many joints, the present study introduces a rock joint constitutive model to capture the transmission and reflection phenomena of blasting stress waves when they reach the joint. At the same time, based on the original FDEM code, an optimized blasting calculation model is proposed. This model considers the effect of explosive gas and accurately describes the physical relationship between the explosive gas pressure and the change in the blasting chamber area caused by crack propagation. To overcome the limitation of previous blasting models that only apply the pressure of the explosive gas to the borehole wall, the present study optimizes the determination conditions for crack penetration and the calculation method for the blasting chamber area as well as further considered the influence of the embedding effect of explosive gas on crack propagation. Finally, through three examples, the transmission and reflection laws of stress waves at the joints and the entire process of rock mass throw blasting are simulated. The results illustrate that this model can capture the propagation of stress waves, the gas wedge effect of explosive gas, and the entire process of crack initiation, propagation, and penetration in the rock mass during the explosion, demonstrating the potential of FDEM in blasting simulation.