It is generally known that discontinuities have a remarkable influence on the mechanical behaviour of rock masses. To further understand the fracture mechanisms of jointed rock masses, substantial effort has been focused on the strength anisotropy and failure characteristics of rocks/rock-like specimens containing persistent joints with different geometric parameters. However, only a few laboratory tests have considered the failure mechanism of a rock mass with 3D joints, especially for non-persistent joints with different persistence levels. In the present work, experiments on cubic rock-like specimens containing non-persistent joints (in areal extent) subjected to uniaxial compression were conducted to further investigate the influence of the joint inclination (θ) and persistence (N) on the rock mechanical properties and failure characteristics. The strength of a 3D non-persistent jointed specimen is characterized by three stages as the joint inclination angle (θ) increases from 0° to 90°. The strength of jointed specimens decreases with increasing N for all θ values, with the highest strength obtained for N = 0.42 and the lowest strength recorded for N = 0.92. Based on CT scan results, four typical fracture modes were identified: splitting, splitting + sliding, sliding, and intact failure. Overall, as the joint inclination increases, the failure mode of the specimen transforms from splitting to sliding and then to the intact failure mode. However, with decreasing joint persistence, the failure modes of some specimens will change from sliding to mixed failure (splitting + sliding).