We present a novel elastomer with an amphiphilic triblock/graft architecture, allowing it to rapidly swell in water and form a tough hydrogel. The design was motivated by uncontrolled hemorrhage, responsible for 80-90% of potentially survivable deaths of US soldiers over the past 15 years. The polymer is 5.7 times as absorbent and 3 times as tough as a state of the art gauze-based hemostatic dressing. It swells to equilibrium within seconds in phosphate buffered saline due to a microphase-separated morphology featuring a continuous mobile ionic phase supported by hydrophobic glassy domains and rubbery linkages, as observed by transmission electron microscopy and small-angle neutron scattering. Thickness-dependent swelling is as much as an order of magnitude faster than many tough hydrogels in the literature, yet toughness is comparable as a function of water content. The polymer is combined with gauze to form a rapidly swelling, fiber-reinforced hydrogel composite with promising mechanical properties.