Livestock grazing is a major driver shaping the biodiversity, functioning, and stability of local grassland communities. Whether grazing impacts on these variables are scale-dependent remains unclear. Here, we conducted a sheep-grazing experiment in a temperate grassland to test grazing effects on the temporal stability of productivity across scales. We found that grazing increased species stability, but substantially decreased local community stability due to reduced asynchronous dynamics among species within communities. The negative effect of grazing on local community stability propagated to reduce stability at larger spatial scales, despite greater spatial asynchrony among communities. By decreasing biodiversity both within and across communities, grazing reduced biodiversity insurance effects and hence the up-scaling of stability from species to communities and further to larger spatial scales. Our study provides the first evidence for the scale-dependence of grazing effects on grassland stability through biodiversity. We suggest that broad-scale ecosystem management regimes should strive to maintain biodiversity across scales to promote ecosystem stability.