The mammalian order Primates is known for widespread sexual dimorphism in size and phenotype. Despite repeated speculation that primate sexual size dimorphism either facilitates or is in part driven by functional differences in how males and females interact with their environments, few studies have directly assessed the influence of sexual dimorphism on performance traits. Here, we use a theoretical morphology framework to show that sexual dimorphism in primate crania is associated with divergent biomechanical performance traits. The degree of dimorphism is a significant covariate in biomechanical trait divergence between sexes. Males exhibit less efficient but stiffer cranial shapes and significant evolutionary allometry in biomechanical performance, whereas females maintain performance stability across their size spectrum. Evolutionary rates are elevated for efficiency in females whereas males emphasize size-dependent cranial stiffness. These findings support a hypothesis of sex-linked bifurcation in masticatory system performance: larger male crania and faster size evolution partially compensate for low efficiency and reflect a de-emphasis of mechanical leverage, whereas female crania maintain higher mechanical efficiency overall and evolve more rapidly in molar-based masticatory performance. The evolutionary checks-and-balances between size dimorphism and cranial mechanical performance may be a more important driver of primate phenotypic evolution than has been hitherto appreciated.