Global biodiversity is under high and rising anthropogenic pressure. Yet, how the taxonomic, phylogenetic, and functional facets of biodiversity are affected by different threats over time is unclear. This is particularly true for the two main drivers of the current biodiversity crisis: habitat destruction and overexploitation. We provide the first long‐term assessment of multifaceted biodiversity changes caused by these threats for any tropical region. Focussing on larger mammals in South America's 1.1 million km2 Gran Chaco region, we assessed changes in multiple biodiversity facets between 1985 and 2015, determined which threats drive those changes, and identified remaining key areas for all biodiversity facets. Using habitat and threat maps, we found, first, that between 1985 and 2015 taxonomic (TD), phylogenetic (PD) and functional (FD) diversity all declined drastically across over half of the area assessed. FD declined about 50% faster than TD and PD, and these declines were mainly driven by species loss, rather than species turnover. Second, habitat destruction, hunting, and both threats together contributed ~57%, ~37%, and ~6% to overall facet declines, respectively. However, hunting pressure increased where TD and PD declined most strongly, whereas habitat destruction disproportionally contributed to FD declines. Third, just 23% of the Chaco would have to be protected to safeguard the top 17% of all three facets. Our findings uncover a widespread impoverishment of mammal species richness, evolutionary history, and ecological functions across broad areas of the Chaco due to increasing habitat destruction and hunting. Moreover, our results pinpoint key areas that should be preserved and managed to maintain all facets of mammalian diversity across the Chaco. More generally, our work highlights how long‐term changes in biodiversity facets can be assessed and attributed to specific threats, to better understand human impacts on biodiversity and to guide conservation planning to mitigate them. [ABSTRACT FROM AUTHOR]