With the development of infrastructure in China, the slope rock mass is affected by external forces such as roads. Tunnel excavation will cause a series of engineering problems, which are essentially caused by the instability caused by the propagation of internal cracks in the rock mass. At the same time, in practical engineering, the rock mass is formed through long-term geological structure, and its internal cracks have a variety of properties. Based on granite samples as the research object, two different angles of sample shapes, cylindrical and circular, are prefabricated. The uniaxial compression test is studied to analyze the law of inclined crack propagation in rock under uniaxial compression. Combined with the theory of fracture mechanics, the influence mechanism of crack inclination and sample shape on crack propagation in rock mass is discussed. The test results show that under uniaxial compression, the stress-strain curves of granite samples can be divided into four stages: compaction, elasticity, plasticity, and residual deformation. For the cylindrical sample, the crack initiation occurs at the tip. The compressive strength of the sample decreases with the increase in the prefabricated crack angle, and the crack initiation angle increases with the increase in the prefabricated crack angle. The fracture of the sample changes from shear slip failure to split shear failure of the penetrating rock mass with the increase in the crack angle. For the disk sample, the crack initiation location gradually increases from the tip to the middle with the increase in the crack angle, and the crack initiation angle increases with the increase in the crack angle. The peak load of the sample decreases first and then increases with the increase in the crack angle and is the minimum at 60°. The fracture mode of the sample is mainly tensile failure. When the crack dip angle is between 30° and 60°, the tensile and shear composite failure of the sample occurs, and the influence mechanism of crack dip angle and sample shape on the crack propagation path is analyzed. The research results have important theoretical significance for engineering design, construction, and stability maintenance.