Spin relaxation and a magnetocaloric effect in a dipolar spin ice Pr2Sn2O7 were investigated by magnetization and alternating susceptibility measurements in Kelvin temperature range and magnetic fields exceeding the estimated value of the saturation field Bsat. An analysis of AC susceptibility revealed existence of two relaxation channels. The calculation of energy spectrum of a single tetrahedron suggests that a fast temperature independent relaxation may be associated with a cross-tunneling process, in which four spins in one tetrahedron are involved. In contrast, a slow relaxation is attributed to a phonon-bottleneck effect. A particle-size analysis identifies a phonon scattering in grain boundaries as a governing mechanism of the phonon bottleneck. Systematic measurements of the magnetization were performed to study magnetocaloric effect in Pr2Sn2O7. A complex analysis of the isothermal change of magnetic entropy ΔSm revealed a dominating effect of magnetocrystalline anisotropy on a magnetocaloric response in an Ising-spin system with a high level of geometrical frustration. The origin of the observed behavior is discussed.