Human activities have altered the species composition of assemblages through introductions and extinctions, but it remains unclear how those changes can affect the different facets of biodiversity. Here we assessed the impact of changes in species composition on taxonomic, functional, and phylogenetic diversity across 281 bird assemblages worldwide. To provide a more nuanced understanding of functional diversity, we distinguished morphological from life‐history traits. We showed that shifts in species composition could trigger a global decline in avian biodiversity due to the high number of potential extinctions. Moreover, these extinctions were not random but unique in terms of function and phylogeny at the regional level. Our findings demonstrated that non‐native species cannot compensate for these losses, as they are both morphologically and phylogenetically close to the native fauna. In the context of the ongoing biodiversity crisis, such alterations in the functional and phylogenetic structure of bird assemblages could heighten ecosystem vulnerability.