The dynamic mechanical properties of deep rock in high underground stress environment have an important influence on the development of deep mine engineering. Therefore, it is of great significance to study its dynamic mechanics. The effects of hydrostatic pressure on the dynamic mechanical properties, energy absorption and damage of white sandstone from a coal mine in Pingdingshan were investigated, using 3D Hopkinson bar experiments and finite element simulations based on the Holmquist-Johnson-Cook (HJC) constitutive model. The results show that as the hydrostatic pressure increases, the peak stress of white sandstone increases. Conversely, the peak strain decreases with the increase of hydrostatic pressure. Furthermore, the hydrostatic pressure can restrain the crack propagation and enhance the strength of white sandstone. Additionally, it was found that the HJC constitutive model can simulate the damage failure of white sandstone well. These expected results provide a valuable reference for the study of dynamic mechanical properties of deep rock and a theoretical basis for the implementation of deep rock engineering.