Nb-doped TiO${}_2$ has attracted considerable attention due to its potential as a colossal permittivity material. Previous studies suggest that its low-temperature colossal permittivity originates from a low polaron hopping energy barrier, which enables rapid flip–flop migration between neighboring Ti sites. In this work, we employ density functional theory (DFT) combined with chemical bond analysis to investigate the effects of hydrostatic pressure and uniaxial strain on polaron hopping in pristine rutile TiO${}_2$ and Nb-doped TiO${}_2$. Under hydrostatic pressure, we find that the hopping energy barrier increases approximately linearly with increasing volume in both systems. This behavior is correlated with pressure-induced modifications of the local Ti environment, which enhance polaron localization. In contrast, uniaxial strain produces a markedly anisotropic response. Pristine TiO${}_2$ exhibits the strongest sensitivity when strain is applied along the hopping direction, whereas Nb-doped TiO${}_2$ shows saturation of the hopping barrier under compressive strain along the same direction. Our findings highlight the mechanical loading as an effective route to tuning polaron hopping and, consequently, the functional properties of TiO${}_2$-based materials.