Idaho’s Snake River Plain is underlain by a young sequence of basaltic lava flows that house one of the most conductive aquifers in the world and have been sculpted by at least three megafloods in the last ∼100 k.y. The timing and routing of these floods, and their interaction with the underlying aquifer, have taken on renewed significance because they have carved amphitheater-headed dry canyons analogous to those found on Mars. In this study, we use cosmogenic 3He and 21Ne dating of flood-deposited boulders to show that the Big Lost River and Bonneville floods were closely spaced in time at ca. 22.3 and ca. 17.5 ka, respectively. Most of the dry canyons record significant erosion during the Big Lost River flood, despite its much smaller magnitude than the later Bonneville flood. We explain this puzzling observation by proposing a composite erosion model in which erosion during the Big Lost River flood was partially accomplished by routing of floodwaters through the Snake River Plain aquifer. Topographic analysis shows that Big Lost River floodwaters ponded in the Terreton Basin, infiltrated into the aquifer, and likely emerged as return flow in watersheds upstream of the dry canyons. We propose that sustained and focused erosion associated with return flow over months to years could explain the unique morphology of some dry canyons. Such a model also explains why most dry canyons are coincident with springs and surface watersheds, and it may provide a model for the way in which morphologically similar canyons evolved on Mars.