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An in-depth understanding of the mechanical properties and damage and fracture mechanism of selected rocks in a diversion tunnel plays an important role in promoting the efficient construction and safety of rock blasting excavation in a diversion tunnel. To study the mechanical properties and damage evolution characteristics of selected rocks in diversion tunnels under uniaxial loading, the uniaxial compression and uniaxial splitting tests of granite and tuff were carried out. In terms of mechanical properties, the evolution characteristics of complete stress-strain curves, instantaneous modulus-strain curves, and input energy density-strain curves were analyzed. In the aspect of damage characteristics, the macroscopic and mesoscopic failure modes were analyzed and the damage fracture mechanism was revealed. Compression-shear failure mainly occurred in granite and tuff under uniaxial compression, showing the characteristics of elastic-brittle fracture failure. Both granite and tuff showed a failure mode of coexistence of “compression-shear failure zone at the loading ends” and “tension-shear failure zone in the middle” under uniaxial splitting. The compression-shear fracture of granite was relatively smooth, and the matrix and mineral particles produced fine particles due to friction in the process of shear slip. The compression-shear fracture of tuff was relatively rough and the characteristics of shear slip were not prominent enough. The fracture failure of granite and tuff was mainly caused by the common fracture of rock matrix and mineral particles. Based on the Lemaitre equivalent strain principle, the pre-peak-post-peak two-stage damage constitutive model established by Weibull statistical distribution theory can accurately describe the static stress-strain relationships of granite and tuff under uniaxial compression.