Spatiotemporal interactions between predators and prey are central to maintaining sustainable functioning ecosystems and community stability. For wild ungulates and their predators, livestock grazing is an important anthropogenic disturbance causing population declines and modifying their interactions over time and space. However, it is poorly understood how fine‐scale grazing affects the spatiotemporal responses of predators, prey, and their interactions. Two opposing hypotheses describe a dichotomy of possible effects. The human shield hypothesis states that people can protect prey because predators avoid areas with high human‐induced mortality risk, whereas in the human competitor hypothesis, humans compete for prey and negatively impact predators through reduced prey availability. We used camera‐trapping data from the Gansu Qilianshan National Nature Reserve in Northwest China to measure occupancy, daily activity patterns, and spatiotemporal interactions between snow leopards (Panthera uncia), the dominant predator, and their ungulate prey in areas with contrasting grazing intensities. The results of grazing were consistent with both the human‐shield and human‐competitor hypotheses, affecting spatiotemporal patterns and interactions of predators and prey. For the primary prey species, blue sheep (Pseudois nayaur), their spatial and temporal patterns were affected by grazing, which led to a reduction in interaction frequencies with snow leopards. For secondary prey, grazing led to reduced interaction frequencies with snow leopards for white‐lipped deer (Przewalskium albirostris) and red deer (Cervus yarkandensis), but increased frequencies for alpine musk deer (Moschus chrysogaster). Our results indicate how both competition among livestock and prey and predator or prey avoidance of grazed areas can impact populations and predator–prey interactions. Our findings are relevant to grazing management and snow leopard conservation.