Positive relationships between biodiversity and ecosystem functioning (BEF) highlight the importance of conserving biodiversity to maintain key ecosystem functions and associated services. Although natural systems are rapidly losing biodiversity due to numerous human-caused stressors, our understanding of how multiple stressors influence BEF relationships comes largely from small, experimental studies. Here, using remote assemblages of coral reef fishes, we demonstrate strong, non-saturating relationships of biodiversity with two ecosystem functions: biomass and productivity. These positive relationships were robust both to an extreme heatwave that triggered coral bleaching and to invasive rats which disrupt nutrient subsidies from native seabirds. Despite having only minor effects on BEF relationships, both stressors still decreased ecosystem functioning via other pathways. The extreme heatwave reduced biodiversity, which, due to the strong BEF relationships, ultimately diminished both ecosystem functions. Conversely, the loss of cross-system nutrient subsidies directly decreased biomass. These results demonstrate multiple ways by which human-caused stressors can reduce ecosystem functioning, despite robust BEF relationships, in natural high-diversity assemblages. © 2020, The Author(s), under exclusive licence to Springer Nature Limited.