Cold and pressure denaturation are believed to have their molecular origin in hydrophobic interactions between nonpolar groups and water. However, the direct characterization of the temperature- and pressure-dependent variations of those interactions with atomistic simulations remains challenging. We investigated the role of solvent in the cold and pressure denaturation of a model hydrophobic 32-mer polymer by performing extensive coarse-grained molecular dynamics simulations including explicit solvation. Our simulations showed that the water-excluded folded state of this polymer is marginally stable and can be unfolded by heating or cooling, as well as by applying pressure, similar to globular proteins. We further detected essential population of a hairpin-like configuration prior to the collapse, which is consistently accompanied by a vapor bubble at the elbow of the kink. Increasing pressure suppresses formation of this vapor bubble by reducing water fluctuations in the hydration shell of the polymer, thus promoting unfolding. Further analysis revealed a slight reduction of water tetrahedrality in the polymer hydration shell compared to the bulk. Cold denaturation is driven by an enhanced tetrahedral ordering of hydration shell water than bulk water. At elevated pressures, the strikingly reduced fluctuations combined with the increase in interstitial water molecules in the polymer hydration shell contribute to weakening of hydrophobic interactions, thereby promoting pressure unfolding. These findings provide critical molecular insights into the changes in hydrophobic hydration during cold and pressure unfolding of a hydrophobic polymer, which is strongly related to the cold and pressure denaturation of globular proteins.