In high-altitude cold areas, freeze-thaw (F-T) cycles induced by day-night and seasonal temperature changes cause numerous rock mass slope engineering disasters. To investigate the dynamic properties of rock in the natural environment of a high-altitude cold area, standard specimens were drilled from the slope of the Jiama copper mine in Tibet, and dynamic compression tests were performed on water-saturated and frozen sandstone with different numbers of F-T cycles (0, 10, 20, 30, and 40) by the split Hopkinson pressure bar (SHPB) system with a cryogenic control system. The influence of water-saturated and frozen conditions on the dynamic performance of sandstone was investigated. The following conclusions are drawn: (1) With increasing strain rate, the attenuation factor (λa) of water-saturated sandstone and the intensifying factor (λi) of frozen sandstone linearly increase. As the number of F-T cycles increases, the dependence factor (λd) of water-saturated sandstone linearly decreases, whereas the λd of frozen sandstone linearly increases. (2) The prediction equation of the dynamic compressive strength of water-saturated and frozen sandstone is obtained, which can be used to predict the dynamic compressive strength of sandstone after various F-T cycles based on the strain rate. (3) The mesoscopic mechanism of water-saturated and frozen sandstone's dynamic compressive strength evolution is investigated. The water softening effect causes the dynamic compressive strength of water-saturated sandstone to decrease, whereas the strengthening effect of pore ice causes it to increase. (4) The decrease in the relative dynamic compressive strength of water-saturated sandstone and the increase in the relative dynamic compressive strength of frozen sandstone can be attributed to the increased porosity.