Non-coplanar and discontinuously jointed rock masses are more complex than coplanar and discontinuously jointed rock masses. The mechanical properties and propagation mechanisms of non-coplanar and discontinuous joints were studied via direct shear tests with microscopic numerical simulation experiments. The numerical simulation tests were performed under different normal stresses, joint inclination angles, and shear rates. The numerical experimental results show that the microscale failure of non-coplanar and discontinuously jointed rock masses is mainly caused by tensile cracks. Additionally, when the peak shear stress is reached, the growth rate of cracks increases rapidly, and the number of cracks increases with increasing normal stress. The shear strength of non-coplanar and discontinuously jointed rock masses increases with increasing normal stress. Under the same normal stress, the variation curves of the shear strength of non-coplanar and discontinuously jointed rock masses with respect to the dip angle exhibit an “S”-shaped nonlinear pattern. Rock masses with joint inclination angles of approximately 15° and 65° have minimum and maximum shear strengths, respectively. The joint dip angle has a significant impact on the final failure mode of rock bridges in the rock mass. As the joint dip angle increases, the final failure modes of rock bridges change from “end-to-end” connection to a combination of “head-to-head” and “tail-to-tail” connections. The shear rate has a certain impact on the peak shear stress, but the impact is not significant. The spatial distribution of the tensile force chains changes as shearing progresses, and stress concentration occurs at the tips of the original joints, which is the reason for the development of long tensile cracks in the deeper parts.