Under the right conditions, some biological systems can maintain high viability after being frozen and thawed, but many others (e.g., organs and many mammalian cells) cannot. To increase the rates of post-thaw viability and widen the library of living cells and tissues that can be stored frozen, an improved understanding of the mode of action of polymeric cryoprotectants is required. Here, we present a polymeric cryoprotectant, poly(methyl glycidyl sulfoxide) (PMGS), that achieved higher post-thaw viability for fibroblast cells than its small-molecule analogue dimethyl sulfoxide. By limiting the amount of water that freezes and facilitating cellular dehydration after ice nucleation, PMGS mitigates the mechanical and osmotic stresses that the freezing of water imparts on cells and facilitates higher-temperature vitrification of the remaining unfrozen volume. The development of PMGS advances a fundamental physical understanding of polymer-mediated cryopreservation, which enables new material design for long-term preservation of complex cellular networks and tissue.