Analyzing the propagation dynamics from meteorological drought (MD) to hydrological drought (HD) is essential for sustainable water resource management, particularly under climate change. This study analyzed the multidimensional propagation characteristics and their driving factors from MD to HD in the Jialing River Basin from 1993 to 2020. The temporal characteristics of drought propagation were analyzed using monthly and daily drought indices, with a focus on variations in initiation lag times across seasons and drought grades. The attenuation and amplification effects during drought propagation were quantified using event propagation ratios, while examining the differential propagation patterns across different drought grades. Additionally, the Geographical Detector Model was employed to identify the main drivers of spatial heterogeneity in hydrological drought response rates. The main findings are as follows: (1) at the daily scale, the initiation stage had the shortest lag, while peak and termination stages showed longer lags. Seasonal and drought grade variations were observed in the initiation lag, with shorter lags in summer and autumn. (2) Drought propagation from MD to HD resulted in an attenuation of maximum intensity, while duration and severity were amplified. (3) Spatial heterogeneity in HD response rate was mainly influenced by evaporative conditions, vegetation cover, and topography.