To investigate the coupling damage characteristics of rock after high-temperature treatment under impact load, dynamic uniaxial compression tests for deep sandstone specimen under laboratory conditions varying with high temperature (i.e., 25°C, 100°C, 300°C, 500°C, 700°C, and 900°C) and strain rate (i.e., 170 s-1, 205 s-1, and 240 s-1) were performed using splitting Hopkinson pressure bar (SHPB) system. Coupling damage variable of deep sandstone was deduced based on the Lemaitre equivalent strain theory. Moreover, the damage parameters of deep sandstone were systematically determined according to the test data, and the effects of high temperature and strain rate on damage growth curves were investigated. Finally, a dynamic compound damage constitutive model, which could consider the coupling damage, was established and verified to describe the dynamic mechanical characteristic of deep sandstone. Theoretical and experimental results indicated that the simulated stress-strain curves matched the test data well and the proposed coupling damage constitutive model could reflect the high temperature-induced weakening and strain rate strengthening effect.