Mountains composed of granite are generally regarded as stable geological formations. However, in Alpine and high-altitude mountains in the eastern part of the Tibetan Plateau, geological hazards such as collapses and landslides occur frequently due to the deterioration of granite mechanical properties caused by the freeze–thaw cycles. To investigate this phenomenon, a freeze–thaw cyclic mechanical test is conducted on granite from the Basu area, and the rock’s damage trend during the freeze–thaw process is analyzed through wave velocity and nuclear magnetic resonance (NMR) tests. The results indicated that the internal damage of granite increases and its wave velocity decreases significantly with increasing the freeze–thaw cycles, implying a decline in the rock’s integrity. Furthermore, the development pattern of the NMR T2 relaxation time distribution indicates that the crack size range of naturally weathered rock samples further increased after freeze–thaw cycles, whereas less-weathered rocks showed a more concentrated range of crack sizes. Triaxial compression tests conducted on rock samples after the freeze–thaw cycles showed that parameters such as the uniaxial compressive strength, elastic modulus, internal friction angle, and cohesion of the rock decreased with increasing freeze–thaw cycles, while a significant change of Poisson’s ratio was not observed. Based on the test data and theoretical analysis, a freeze–thaw damage constitutive model of the Basu granite can be established to simulate and predict the overall variation in rock stress and strain under various confining pressures and freeze–thaw cycles. Hopefully, the present study will provide useful guidance for research on the hazard mechanism and hazard prevention of granite sand-sliding slopes in the Basu area.