The exploitation of mineral resources is gradually shifting from shallow to deep targets. However, the corresponding basic theoretical research has not determined the differences in rock-mining engineering at different depths. In this paper, longitudinal wave velocity measurements, uniaxial compression tests, and dynamic impact tests were conducted on granite from various burial depths to reveal the static and dynamic mechanical properties of the rocks. The initial damage variables of the rock specimens decrease after a rapid increase with increasing burial depth. The stress–strain curves of the deep rocks for various strain rates can be divided into two modes. The relationships between the secant modulus, peak stress, elastic modulus, and burial depth basically follow a quadratic function. The rock failure patterns observed in the uniaxial compression tests are basically tensile. In the dynamic loading experiments at various strain rates, the failure pattern of the rock changes with burial depth, when the strain rate is small, from local instability to overall instability and back to local instability; while the strain rate increases, the failure pattern transforms into overall instability. In the dynamic impact experiments with different confining pressures, the rock only undergoes shear failure due to the restriction of the lateral deformation from the confining pressure. These research achievements could provide significant theoretical support for rockburst prevention at greater mining depths.