There is increasing evidence that mixed-species forests can provide multiple ecosystem services at a higher level than their monospecific counterparts. However, most studies concerning tree diversity and ecosystem functioning relationships use data from forest inventories (under noncontrolled conditions) or from very young plantation experiments. Here, we investigated temporal dynamics of diversity–productivity relationships and diversity–stability relationships in the oldest tropical tree diversity experiment. Sardinilla was established in Panama in 2001, with 22 plots that form a gradient in native tree species richness of one-, two-, three- and five-species communities. Using annual data describing tree diameters and heights, we calculated basal area increment as the proxy of tree productivity. We combined tree neighbourhood- and community-level analyses and tested the effects of both species diversity and structural diversity on productivity and its temporal stability. General patterns were consistent across both scales indicating that tree–tree interactions in neighbourhoods drive observed diversity effects. From 2006 to 2016, mean overyielding (higher productivity in mixtures than in monocultures) was 25%–30% in two- and three-species mixtures and 50% in five-species stands. Tree neighbourhood diversity enhanced community productivity but the effect of species diversity was stronger and increased over time, whereas the effect of structural diversity declined. Temporal stability of community productivity increased with species diversity via two principle mechanisms: asynchronous responses of species to environmental variability and overyielding. Overyielding in mixtures was highest during a strong El Niño-related drought. Overall, positive diversity–productivity and diversity–stability relationships predominated, with the highest productivity and stability at the highest levels of diversity. These results provide new insights into mixing effects in diverse, tropical plantations and highlight the importance of analyses of temporal dynamics for our understanding of the complex relationships between diversity, productivity and stability. Under climate change, mixed-species forests may provide both high levels and high stability of production.