Morphological responses of nonmammalian herbivores to external ecological drivers have not been quantified over extended timescales. Herbivorous nonavian dinosaurs are an ideal group to test for such responses, because they dominated terrestrial ecosystems for more than 155 Myr and included the largest herbivores that ever existed. The radiation of dinosaurs was punctuated by several ecologically important events, including extinctions at the Triassic/Jurassic (Tr/J) and Jurassic/Cretaceous (J/K) boundaries, the decline of cycadophytes, and the origin of angiosperms, all of which may have had profound consequences for herbivore communities. Here we present the first analysis of morphological and biomechanical disparity for sauropodomorph and ornithischian dinosaurs in order to investigate patterns of jaw shape and function through time. We find that morphological and biomechanical mandibular disparity are decoupled: mandibular shape disparity follows taxonomic diversity, with a steady increase through the Mesozoic. By contrast, biomechanical disparity builds to a peak in the Late Jurassic that corresponds to increased functional variation among sauropods. The reduction in biomechanical disparity following this peak coincides with the J/K extinction, the associated loss of sauropod and stegosaur diversity, and the decline of cycadophytes. We find no specific correspondence between biomechanical disparity and the proliferation of angiosperms. Continual ecological and functional replacement of pre-existing taxa accounts for disparity patterns through much of the Cretaceous, with the exception of several unique groups, such as psittacosaurids that are never replaced in their biomechanical or morphological profiles.