Using quasi-elastic neutron scattering (QENS), we study the dynamics of water in a concentrated poly(N-isopropylacrylamide) solution over a large temperature range across the demixing transition at pressures of 0.1 and 130 MPa. The QENS spectra extending in frequency from 1 to 3 x 10(3) GHz and in momentum transfer from 0.45 to 1.65 angstrom(-1) reveal the relaxation of hydration water as well as multiple dynamic processes in bulk water. At the cloud point, the fraction of hydration water decreases abruptly at 0.1 MPa, whereas at 130 MPa, it decreases smoothly. The susceptibility spectra of hydration water occur at lower frequencies than those of pure water and the dependence of the relaxation times on momentum transfer can be described by a jump-diffusion model. At a pressure of 0.1 MPa, the hydration water remaining in the two-phase region is more constrained than at 130 MPa. We attribute these findings to the pressure-dependent hydration interactions.