In the propagation from meteorological to hydrological drought, there are time-lag and step-abrupt effects, quantified in terms of propagation time and threshold, which play an important role in hydrological drought early warning. However, seasonal drought propagation time and threshold and their dynamics as well as the corresponding driving mechanism remain unknown in a changing environment. To this end, the standardized precipitation index (SPI) and standardized runoff index (SRI) were used respectively to characterize meteorological and hydrological droughts and to determine the optimal propagation time. Then, a seasonal drought propagation framework based on Bayesian network was proposed for calculating the drought propagation threshold with SPI. Finally, the seasonal dynamics and preliminary attribution of propagation characteristics were investigated based on the random forest model and correlation analysis. The results show that 1) relatively short propagation time (less than 9 months) and large propagation threshold (from −3.18 to −1.19) can be observed in the Toxkan River basins (subbasin II), especially for spring, showing low drought resistance; 2) drought propagation time shows an extended trend in most seasons, while the drought propagation threshold displays an increasing trend in autumn and winter in the Aksu River basin (subbasins I–II), and the opposite characteristics in the Hotan and Yarkant River basins (subbasins III–V); and 3) the impacts of precipitation, temperature, potential evapotranspiration, and soil moisture on drought propagation dynamics are inconsistent across subbasins and seasons, noting that reservoirs serve as a buffer to regulate the propagation from meteorological to hydrological droughts. The findings of this study can provide scientific guidelines for watershed hydrological drought early warning and risk management.