Humid tropical forests play a dominant role in the functioning of Earth but are under increasing threat from changes in land use and climate. How forest vulnerability varies across space and time and what level of stress forests can tolerate before facing a tipping point are poorly understood. Here, we develop a tropical forest vulnerability index (TFVI) to detect and evaluate the vulnerability of global tropical forests to threats across space and time. We show that climate change together with land-use change have slowed the recovery rate of forest carbon cycling. Temporal autocorrelation, as an indicator of this slow recovery, increases substantially for above-ground biomass, gross primary production, and evapotranspiration when climate stress reaches a critical level. Forests in the Americas exhibit extensive vulnerability to these stressors, while in Africa, forests show relative resilience to climate, and in Asia reveal more vulnerability to land use and fragmentation. TFVI can systematically track the response of tropical forests to multiple stressors and provide early-warning signals for regions undergoing critical transitions.