The stability of damaged rock mass is a critical problem in the control of surrounding rock in underground engineering. As the main macroscopic defect of rock surrounding engineering, it is of great significance to study its propagation mechanism and the experimental characteristics of rock mechanics. Surface-fractured rock mass is a typical representative of three-dimensional fracture. To reveal the failure mechanism of surface-fractured rock mass, a three-dimensional mechanical failure model of a surface-fractured rock specimen was established, including the initiation, crack propagation, and cooperative deformation of the rock micro-element. Taking the depth of the surface horizontal fissure as a variable, standard rock specimens with surface horizontal fissures of different depths were prepared, and an experimental study of surface-fractured rock specimens was carried out. The RMT rock mechanics test system was used to perform uniaxial compression tests on standard specimens containing fractured rock specimens of different depths. The complete stress–strain curves of samples with different fracture depths were obtained, and the influence of different fracture depths on rock strength and deformation characteristics was analyzed. The crack initiation, propagation, and failure modes of the specimens under uniaxial compression were analyzed based on high-speed camera technology. Through the combination of 3D image processing and acoustic emission monitoring, differences between failure before and after the peak in both asymmetrically damaged rock specimens and symmetrically damaged rock specimens were found. The mechanism of weak strength and weak stability of asymmetrically damaged rock specimens after the peak was explained theoretically. The research results showed that the existence of the horizontal joint plane directly led to a significant reduction in the strength of the jointed rock sample, and the fracture depth played an important role in controlling the failure mode of the jointed rock specimens. The uniaxial compression of rock specimens with horizontal non-penetrating surface fissures produced three-dimensional failure modes, and the depth of surface fissures changed the failure mode of the specimens under uniaxial compression. As the crack depth increased, the failure mode of the specimen changed from tensile failure to shear failure. The surface crack sample showed regional asymmetric failure and poor structural stability.