The capability to perform high-pressure low-temperature nuclear inelastic scattering on ¹²⁵Te and ¹²¹Sb with a sapphire backscattering monochromator is presented. This technique was applied to measure nuclear inelastic scattering in TeO₂ at pressures up to 10 GPa and temperatures down to 25 K. The evaluated partial Te densities of phonon states were compared with theoretical calculations and with Raman scattering measured under the same conditions. The high-pressure cell developed in this work can also be used for other techniques at pressures up to at least 100 GPa.