The Loess Plateau frequently endures droughts, and the propagation process has grown more intricate due to the interplay of climate change and human activities. This study developed the Standardized Precipitation Evapotranspiration Index (SPEI) and the Standardized Soil Moisture Index (SSMI) on a 3-month scale and examined the spatiotemporal characteristics and driving mechanisms of drought propagation from meteorological to agricultural drought utilizing cross-wavelet analysis, grey relational analysis, and the optimal parameter-based geographical detector (OPGD) model. The results demonstrate a substantial seasonal correlation between meteorological and agricultural droughts in spring, summer, and autumn, as evidenced by cross-wavelet coherence analysis (wavelet coherence > 0.8, p < 0.05). Lag analysis utilizing grey relational degree (>0.8) indicates that drought propagation generally manifests with a temporal delay of 1–3 months, with the shortest lag observed in spring (average 1.2 months) and the longest in winter (average 3.1 months). Distinct spatial heterogeneity is seen within geomorphological divisions: the loess wide valley hills and loess beam hills divisions exhibit the highest propagation rates (0.64 and 0.59), whereas the loess tableland and soil–stone hills divisions have lower propagation (around 0.50). The OPGD results reveal that precipitation, soil moisture, and temperature are the principal contributing factors, although their effects differ among geomorphological types. Interactions among components exhibit synergistic enhancement effects. This study improves our comprehension of seasonal and geomorphological heterogeneity in drought propagation from meteorological to agricultural droughts and provides quantitative evidence to support early drought warnings across various divisions, agricultural risk assessment, and water security strategies in the Loess Plateau.