Understanding fine‐scale assemblage composition patterns of mammals is important to increase ecological knowledge and support conservation actions. We investigated whether β‐diversity of medium and large‐sized mammals and its components (replacement and richness difference) are related to distance to major rivers, height above the nearest drainage (HAND), and vegetation height; and whether species interactions shape their spatiotemporal distribution. We used camera traps to monitor the mammal assemblage of the Tumucumaque Mountains National Park, Northeastern Amazon. The difference (Δ) in distance to major rivers and geographic distance between sites affected positively the total β‐diversity and both its components. ΔVegetation height affected total β‐diversity and species replacement, while ΔHAND affected richness differences, and to a lower extent, species replacement. We found evidence that spotted pacas (Cuniculus paca) and ocelots (Leopardus pardalis) adjust their spatiotemporal dynamics to escape from predation and to overlap with abundant prey, respectively. However, we did not find evidence that competition affects the spatiotemporal distribution of any other species. Vegetation height, distance to rivers and HAND influenced mammal assemblages probably through shaping the quality and amount of resources. Predation risk seems to be important in shaping the use of time and space by prey, while the distribution of prey is important for the use of time and space for predators. Furthermore, other niche differentiation mechanisms may explain why competition did not affect the species' spatiotemporal dynamics. We highlight the need to include different environmental contexts within protected areas to promote mammal diversity and conservation.