Functional trade-offs can affect patterns of morphological and ecological evolution as well as the magnitude of morphological changes through evolutionary time. Using morpho-functional landscape modelling on the cranium of 132 carnivore species, we focused on the macroevolutionary effects of the trade-off between bite force and bite velocity. Here, we show that rates of evolution in form (morphology) are decoupled from rates of evolution in function. Further, we found theoretical morphologies optimising for velocity to be more diverse, while a much smaller phenotypic space was occupied by shapes optimising force. This pattern of differential representation of different functions in theoretical morphological space was highly correlated with patterns of actual morphological disparity. We hypothesise that many-to-one mapping of cranium shape on function may prevent the detection of direct relationships between form and function. As comparatively only few morphologies optimise bite force, species optimising this function may be less abundant because they are less likely to evolve. This, in turn, may explain why certain clades are less variable than others. Given the ubiquity of functional trade-offs in biological systems, these patterns may be general and may help to explain the unevenness of morphological and functional diversity across the tree of life.