Nutrients and herbivores are well-known drivers of grassland diversity and stability in local communities. However, whether they interact to impact the stability of aboveground biomass and whether these effects depend on spatial scales remain unknown. It is also unclear whether nutrients and herbivores impact stability via different facets of plant diversity including species richness, evenness, and changes in community composition through time and space. We used a replicated experiment adding nutrients and excluding herbivores for 5 years in 34 global grasslands to explore these questions. We found that both nutrient addition and herbivore exclusion alone reduced stability at the larger spatial scale (aggregated local communities; gamma stability), but through different pathways. Nutrient addition reduced gamma stability primarily by increasing changes in local community composition over time, which was mainly driven by species replacement. Herbivore exclusion reduced gamma stability primarily by decreasing asynchronous dynamics among local communities (spatial asynchrony). Their interaction weakly increased gamma stability by increasing spatial asynchrony. Our findings indicate that disentangling the processes operating at different spatial scales may improve conservation and management aiming at maintaining the ability of ecosystems to reliably provide functions and services for humanity.