Climate change mitigation and biodiversity conservation are key forest functions, but how to pursue them jointly in timber-managed forests is still unclear. We use a Europe-wide dataset of forest multi-taxon diversity and stand structure to (i) evaluate the importance of aboveground carbon stocks in determining species richness of six taxonomic groups; (ii) assess relationships between species richness and carbon stocks; (iii) discuss the potential to jointly enhance carbon and biodiversity and policy implications. Carbon-diversity relationships are positive for several groups, but mostly when deadwood pools are considered. Forest policies should consider the complex relationship between different carbon pools and taxonomic groups. Environmental policies emphasizing carbon sequestration in aboveground living biomass may conflict with biodiversity conservation by promoting homogeneous, fast-growing forests that fail to support species diversity of multiple groups. Sustainable forest management should acknowledge that deadwood carbon instead may translate into positive outcomes for both carbon storage and biodiversity conservation.