The strength of rock mass is significantly affected by the mechanical properties of discontinuities. Therefore, the study of the shear mechanical properties of discontinuities is considered of great significance for the stability and safety evaluation of rock mass engineering. A computational method for characterizing the three-dimensional morphological features of rock discontinuities was proposed, with consideration given to shear direction. Graded cyclic shear tests were conducted on rock discontinuities with different surface morphologies. The influence of surface morphology on the shear mechanical properties of discontinuities was revealed, and a prediction model for the shear strength of rock discontinuities was established by incorporating three-dimensional morphological characteristics. The results show that the proposed three-dimensional roughness coefficient is demonstrated to effectively reflect the morphological characteristics of discontinuities. Compared with traditional methods based on two-dimensional profile lines, better applicability is demonstrated by the proposed method at a three-dimensional scale. The morphological parameters of discontinuities are observed to continuously decrease with increasing numbers of graded cyclic shear cycles. During shearing, three failure modes are exhibited by specimens with different morphological characteristics: ductile failure, brittle fracture, and tooth-gnawing pattern. The deviation rate between the peak shear strength predicted by the proposed model and experimental values is generally controlled within ±10%, indicating good agreement. Thus, good adaptability is shown by the new three-dimensional morphological evaluation parameter in predicting the shear strength of discontinuities. Theoretical basis is provided by the research results for deformation control and advanced protection in rock engineering.