In this study, cement mortar was used to make specimens containing groups of parallel joints with different inclination angles to simulate natural rock mass, and the specimens were subjected to shear tests under different normal stresses. By analyzing the crack propagation path, failure modes, and strength characteristics of these rock specimens, the effects of normal stress and joint inclination angles on the strength and failure characteristics of this type of rock mass were studied. The following conclusions are drawn: 1) when the inclination angles of the joints are 0° and 15°, the changing of the normal stress did not affect the failure mode of the rock mass. The rock mass was mainly in the mode of shear failure, and the increase in the normal stress only increased the spalling area of the rock mass. 2) When the inclination angles of the joints are 30°, 45°, and 60°, with the increasing of the normal stress, the number of those approximately parallel cracks in the specimens increased, the friction marks caused by shearing increased, and the failure mode of the rock mass changed from tension failure to tension–shear composite failure. 3) Under different joint inclination angles, the propagation and penetration paths of cracks generated in the rock mass and the damage mode of the rock mass were different. With an increase in the joint inclination angles, the damage mode of the rock mass gradually changes from shear damage to tensile–shear composite damage and the α and β angles between the through cracks and the vertical direction on the left and right sides of the specimens tended to decrease. 4) The shear resistance of the rock mass was affected by the inclination angle of the joints and the normal pressure. The shear resistance of rock mass was improved due to the increasing of normal stress. Within a certain range, with the increasing of the inclination angles of the joint, the shear resistance of the rock mass tended to decrease first and then to increase.