Morphological diversification does not proceed evenly across the organism. Some body parts tend to evolve at higher rates than others, and these rate biases are often attributed to sexual and natural selection or to genetic constraints. We hypothesized that variation in the rates of morphological evolution among body parts could also be related to the performance consequences of the functional systems that make up the body. Specifically, we tested the widely held expectation that the rate of evolution for a trait is negatively correlated with the strength of biomechanical trade-offs to which it is exposed. We quantified the magnitude of trade-offs acting on the morphological components of three feeding-related functional systems in four radiations of teleost fishes. After accounting for differences in the rates of morphological evolution between radiations, we found that traits that contribute more to performance trade-offs tend to evolve more rapidly, contrary to the prediction. While ecological and genetic factors are known to have strong effects on rates of phenotypic evolution, this study highlights the role of the biomechanical architecture of functional systems in biasing the rates and direction of trait evolution.