Drought propagation mechanisms in sandy lands remain insufficiently understood, particularly regarding the dynamic thresholds and integrated processes linking meteorological, hydrological, and agricultural droughts. To address this gap, this study investigates the spatiotemporal evolution, propagation characteristics, and triggering conditions of drought in the Mu Us Sandy Land (MUSL) from 1982 to 2023. Using the standardized precipitation index (SPI), standardized runoff index (SRI), and standardized soil moisture index (SSMI), we characterized multi-type drought dynamics. Methodologically, we integrated the Mann-Kendall trend test, empirical orthogonal function (EOF) decomposition, run theory, and Copula functions to analyze drought trends, identify drought events, quantify propagation relationships, and determine triggering thresholds. The results show that: (1) drought duration has gradually increased while intensity has decreased, with more severe initial droughts leading to shorter lag times; (2) meteorological-to-hydrological drought events are more intense, whereas meteorological-to-agricultural droughts last longer, with development times of 1 month and 3 months, respectively; (3) the probability of triggering hydrological drought is higher for meteorological droughts shorter than two months, while triggering agricultural drought shows a more uniform duration distribution, and drought triggering probability increases with meteorological drought severity. These findings provide a systematic, threshold-based perspective on drought propagation in sandy ecosystems and offer a scientific basis for dynamic monitoring and early warning.