Cover crops are increasingly being included in crop rotations as a mechanism to promote diversity and provide agroecosystem services, including weed suppression. Recently, cover crop mixtures have increased in popularity in an attempt to provide a greater diversity in ecological services as compared with monocultures. Several recent studies, however, have failed to detect a positive effect of cover crop diversity on biomass production or weed suppression. Here we assessed biomass productivity and weed suppression in 19 cover crops seeded as monocultures and 19 mixtures of varying species composition and functional richness (two- and three-species mixtures) of full-season cover crops in Atlantic Canada. Cover crop biomass production and weed suppression varied by species identity, functional diversity, and species richness. As cover crop biomass increased regardless of diversity, weed biomass declined. Highly productive forbs and grasses provided the greatest weed suppression in monoculture. In line with previous observations, mixtures were not more productive or weed suppressive on average than the most productive monocultures. We observed that the inclusion of the highly productive species buckwheat (Fagopyrum esculentum Moench) and sorghum–sudangrass [Sorghum × drummondi (Nees ex Steud.) Millsp. & Chase] in a mixture increased stand evenness, productivity, weed suppression, and spatiotemporal stability. Taken together, our results suggest that effects of diversity on mixture productivity and weed suppression are species specific. This further demonstrates the importance of species selection in cover crop mixture design.