Climate change is likely to impact multiple dimensions of biodiversity. Species range shifts are expected and may drive changes in the composition of species assemblages. In some regions, changes in climate may precipitate the loss of geographically restricted, niche specialists and facilitate their replacement by more widespread, niche generalists, leading to decreases in β‐diversity and biotic homogenization. However, in other regions climate change may drive local extinctions and range contraction, leading to increases in β‐diversity and biotic heterogenization. Regional topography should be a strong determinant of such changes as mountainous areas often are home to many geographically restricted species, whereas lowlands and plains are more often inhabited by widespread generalists. Climate warming, therefore, may simultaneously bring about opposite trends in β‐diversity in mountainous highlands versus relatively flat lowlands. To test this hypothesis, we used species distribution modelling to map the present‐day distributions of 2669 Neotropical anuran species, and then generated projections of their future distributions assuming future climate change scenarios. Using traditional metrics of β‐diversity, we mapped shifts in biotic homogenization across the entire Neotropical region. We used generalized additive models to then evaluate how changes in β‐diversity were associated with shifts in species richness, phylogenetic diversity and one measure of ecological generalism. Consistent with our hypothesis, we find increasing biotic homogenization in most highlands, associated with increased numbers of generalists and, to a lesser extent, losses of specialists, leading to an overall increase in alpha diversity, but lower mean phylogenetic diversity. In the lowlands, biotic heterogenization was more common, and primarily driven by local extinctions of generalists, leading to lower α‐diversity, but higher mean phylogenetic diversity. Our results suggest that impacts of climate change on β‐diversity are likely to vary regionally, but will generally lead to lower diversity, with increases in β‐diversity offset by decreases in α‐diversity.