Wave impedance is an important physical quantity to characterize the dynamic properties of materials. To explore the influence of wave impedance on the dynamic mechanical response of rock, the granite samples with a wave impedance gradient change are obtained by changing the heating temperature, and the impact compression test is carried out by using a split Hopkinson pressure bar (SHPB) device. The stress wave propagation law, dynamic stress−strain relationship, and fracture characteristics of rocks with different wave impedances are studied comparatively, and the influence mechanism of wave impedance on the dynamic mechanical response of rocks is comprehensively analyzed from two aspects of material properties and dynamics. The results show the following: (1) Under the action of the same incident wave, the reflected wave amplitude, transmission wave takeoff time, peak stress, peak strain, and equivalent average size of fragments of granite samples with different wave impedances are significantly different. ( 2) As the heating temperature increases, the wave impedance of granite continuously decreases and the degree of damage intensifies. Within the high-temperature treatment range of 400 to 600 °C, there is a damage wave impedance threshold between 7854 and 3081 g•cm −3 •m•s −1 . Below this wave impedance, granite will appear to have significant damage deterioration. (3) Under the same incident wave, the strain rate and loading rate of granite samples show negative correlation and positive correlation with wave impedance, respectively. There is a progressive relationship between rock wave impedance, stress wave propagation, strain rate history/stress history, and dynamic mechanical response.