To study the dynamic mechanical properties and failure characteristics of intersecting jointed rock masses with different joint distributions under confining pressure, considering the cross angle α and joint persistence ratio η, a numerical model of the biaxial Hopkinson bar test system was established using the finite element method–discrete-element model coupling method. The validity of the model was verified by comparing and analyzing it in conjunction with laboratory test results. Dynamics-static combined impact tests were conducted on specimens under various conditions to investigate the strength characteristics and patterns of crack initiation and expansion. The study revealed the predominant factors influencing intersecting joints with different angles and penetrations under impact loading. The results show that the peak stress of the specimens decreases first and then increases with the increase of the cross angle. When α < 60°, regardless of the value of η, the dynamic stress of the specimens is controlled by the main joint. When α ≥ 60°, the peak stress borne by the specimens decreases with increasing η. When α < 60°, the initiation and propagation of cracks in the cross-jointed specimens are mainly controlled by the main joint, and the final failure surface of the specimens is composed of the main joint and wing cracks. When α ≥ 60° or η ≥ 0.67, the secondary joint guides the expansion of the wing cracks, and multiple failure surfaces composed of main and secondary joints, wing cracks, and co-planar cracks are formed. Increasing lateral confinement significantly increases the dynamic peak stress able to be borne by the specimens. Under triaxial conditions, the degree of failure of the intersecting jointed specimens is much lower than that under uniaxial and biaxial conditions.