Climate extremes such as droughts are expected to increase in frequency and intensity with global change. Therefore, it is important to map and predict ecosystem responses to such extreme events to maintain ecosystem functions and services. Alongside abiotic factors, biotic factors such as the proportion of needle and broadleaf trees were found to affect forest drought responses, corroborating results from biodiversity–ecosystem functioning (BEF) experiments. Yet it remains unclear to what extent the behavior of non-experimental systems at large scales corresponds to the relationships discovered in BEF experiments. Using remote sensing, the trait-based functional diversity of forest ecosystems can be directly quantified. We investigated the relationship between remotely sensed functional richness and evenness and forest drought responses using data from temperate mixed forests in Switzerland, which experienced an extremely hot and dry summer in 2018. We used Sentinel-2 satellite data to assess aspects of functional diversity and quantified drought response in terms of resistance, recovery, and resilience from 2017 to 2020 in a scalable approach. We then analyzed the BEF relationship between functional diversity measures and drought response for different aggregation levels of richness and evenness of three physiological canopy traits (chlorophyll, carotenoid/chlorophyll ratio, and equivalent water thickness). Forest stands with greater trait richness were more resistant and resilient to the drought event, and the relationship of trait evenness with resistance or resilience was hump-shaped or negative, respectively. These results suggest forest functional diversity can support forests in such drought responses via a mixture of complementarity and dominance effects, the first indicated by positive richness effects and the second by negative evenness effects. Our results link ecosystem functioning and biodiversity at large scales and provide new insights into the BEF relationships in non-experimental forest ecosystems.