Drought incidents and the pressure on water resources have increased in recent years, which has threatened sustainable development. Recently, research has been conducted on drought propagation. However, few studies have investigated the characteristics and mechanisms of drought propagation in plateau mountainous regions with complex topography, which limits the efforts to mitigate drought. We used the Longchuan River Basin (LRB) in Southwest China as a case study to analyze the spatiotemporal variations of meteorological, hydrological, and agricultural droughts and the process of drought propagation in plateau mountainous regions. Our results demonstrated that: (1) the variation in the intensity, frequency, and coverage of droughts indicated that meteorological droughts and hydrological droughts were increasingly serious, while agricultural droughts were eased from 2000 to 2015; (2) the propagation time between different types of droughts was approximately 2 months; and (3) the propagation sequences of droughts varied by altitude; in particular, agricultural droughts propagated to hydrological droughts at higher altitudes, and the opposite occurred at lower altitudes. We concluded that elevation plays a critical role in the time-space differentiation of drought propagation in plateau mountains. More attention should be paid to the spatial differentiation of drought propagation based on land use under different topographic conditions. The results of this study can provide a new perspective for future drought propagation studies.