Sustainable tourism is increasingly threatened by compound climate extremes, but how these hazards propagate through destination networks is poorly understood. This study quantifies the direct and cross-boundary spillover effects of compound climate extremes on tourism demand in Sichuan Province, China, by integrating 75 years of high-resolution ERA5 reanalysis data with an 11-year municipal panel dataset (2014–2024, N = 21). Employing a gravity center migration model and a two-way fixed-effects spatial econometric model, we find that prolonged droughts impose a significant direct local damage on tourism, while wet-hot compound events generate a substantial positive spatial spillover, indicating that tourists spatially substitute toward cooler neighboring destinations rather than cancelling travel. By contrast, drought and dry-hot events produce negative spillovers consistent with regional brand contagion. These contrasting propagation mechanisms (spatial substitution versus contagion) depend fundamentally on event type and are invisible to conventional non-spatial models. Our findings directly inform global sustainable development objectives related to climate action and economic growth, offering an evidence base for spatially coordinated, event-specific climate adaptation strategies in mountain tourism networks facing accelerating climate risks.