The taxonomic, phylogenetic and trait dimensions of betadiversity each provide unique insight into the importance of historical isolation and environmental conditions in shaping global diversity. These three dimensions should, in general, be positively correlated. However, if similar environmental conditions filter species with similar trait values, then assemblages located in similar environmental conditions, but separated by large dispersal barriers, may show high taxonomic, high phylogenetic, but low trait betadiversity. Conversely, we expect lower phylogenetic diversity but higher trait biodiversity among assemblages that are connected but are in differing environmental conditions. We calculated all pairwise comparisons of ~110x110 km grid-cells across the globe for ~5,000 mammal species (~70 million comparisons). We considered realms as units representing geographic distance and historical isolation and biomes as units with similar environmental conditions. While betadiversity dimensions were generally correlated, we highlight geographic regions of decoupling among betadiversity dimensions. Our analysis shows that assemblages from tropical forests in different realms had low trait dissimilarity while phylogenetic betadiversity was significantly higher than expected, suggesting potential convergent evolution. Low trait betadiversity was surprisingly not found between isolated deserts, despite harsh environmental conditions. Overall, our results provide evidence for parallel assemblage structure of mammal assemblages driven by environmental conditions at a global scale.