Current theory proposes that healthy neural dynamics operate in a metastable regime, where brain regions interact to simultaneously maximize integration and segregation. Metastability may confer important behavioral properties, such as cognitive flexibility. It is increasingly recognized that neural dynamics are constrained by the underlying structural connections between brain regions. An important challenge is, therefore, to relate structural connectivity, neural dynamics, and behavior. Traumatic brain injury (TBI) is a pre-eminent structural disconnection disorder whereby traumatic axonal injury damages large-scale connectivity, producing characteristic cognitive impairments, including slowed information processing speed and reduced cognitive flexibility, that may be a result of disrupted metastable dynamics. Therefore, TBI provides an experimental and theoretical model to examine how metastable dynamics relate to structural connectivity and cognition. Here, we use complementary empirical and computational approaches to investigate how metastability arises from the healthy structural connectome and relates to cognitive performance. We found reduced metastability in large-scale neural dynamics after TBI, measured with resting-state functional MRI. This reduction in metastability was associated with damage to the connectome, measured using diffusion MRI. Furthermore, decreased metastability was associated with reduced cognitive flexibility and information processing. A computational model, defined by empirically derived connectivity data, demonstrates how behaviorally relevant changes in neural dynamics result from structural disconnection. Our findings suggest how metastable dynamics are important for normal brain function and contingent on the structure of the human connectome.