The propagation of stress waves and the evolution of blasting-induced cracks in discontinuous rock mass are strongly influenced by joint characteristics. This study focuses on intersecting-joint rock mass and employs the explicit dynamic finite element method with the RHT constitutive model to simulate blasting. The effects of joint thickness and angle on stress wave behavior and crack propagation were systematically analyzed, and fractal theory was applied using MATLAB 2023b to quantitatively characterize crack distribution. The results indicate that joint thickness significantly affects stress wave transmission and reflection: thicker joints enhance reflected wave intensity while attenuating transmitted waves due to successive reflections within the infill. Joint angle controls the number of reflections between joints, with smaller angles producing stronger interactions. Thickness and angle jointly govern crack propagation, causing cracks to concentrate between the borehole and joints. Thickness primarily determines crack density on the blast-facing side of horizontal joints, whereas joint angle exerts deflecting and inhibiting effects. Fractal analysis shows that the fractal dimension of cracks varies nonlinearly with joint characteristics, with higher values in the borehole-to-joint region, increasing with thickness and angle. These findings provide quantitative insight into stress wave–joint interactions and guidance for optimizing blasting design in jointed rock mass, helping to minimize overbreak and underbreak and improve excavation safety.