Forest ecosystems provide key ecological, social, and climate benefits, yet their functions are potentially threatened by rising compound extremes characterised by simultaneous heat and drought or moisture excess. Here, we explore how forests resist and recover from compound heat and moisture extremes and how tree diversity mediates these responses, using U.S. forest inventory data along with satellite-based stability estimates. We find that compound extremes result in lower forest resistance and recovery than individual extremes. Compound extremes tend to exhibit synergistic effects, causing greater negative impacts than the sum of individual extremes. Compound heat and drought have slightly stronger destabilising effects than compound heat and moisture excess. Higher tree diversity consistently improves resistance and recovery under both individual and compound extremes. Our findings suggest that focusing solely on individual climate extremes is likely to underestimate the impacts of compound extremes and to increase uncertainty in projections of terrestrial carbon-cycle feedbacks, while also highlighting the critical role of tree diversity in mitigating these threats under future climate conditions.