Climate change and anthropogenic influences amplify drought complexity, entangle non‐stationarity (NS) and further challenge drought comprehension. This study aims to understand the dynamic evolution of drought propagation patterns due to climatic and anthropogenic pressures by assessing the non‐stationary linkages between hydrological variables and drought characteristics. It employs four standardized drought indicators to comprehensively examine the spatio‐temporal evolution of meteorological (MD) and hydrological (HD) drought characteristics. Data from 29 semi‐arid catchments from six river basins in Peninsular India, are analyzed to uncover distinct drought propagation patterns. This study utilizes a novel Non‐overlapping Block‐stratified Random Sampling (NBRS) approach to detect NS in drought characteristics and hydrological variables, shedding light on the underlying drivers of this dynamic behavior. The results indicate similarities in drought behavior for the Sabarmati, Mahi and Tapi (SMT) basins compared with the Godavari, Krishna and Pennar (GKP) basins, with shorter (longer) propagation times noted for SMT (GKP) basins. While HD severity decreases over time in SMT basins, it intensifies in GKP basins, which are linked to intensive anthropogenic interventions such as river regulation and reservoir operations, thus resulting in prolonged and intensified droughts. Rainfall primarily exhibits time‐invariance, while significant NS is observed in potential evapotranspiration (particularly in the Krishna and Pennar basins), streamflow and baseflow across all basins. The study also identified three distinct drought propagation patterns in these basins, highlighting cases where MD did not transition to HD, instances of HD occurring without preceding MD and synchronous propagation of MD to HD. The study outcomes provide profound insights into the evolution of drought dynamics under climatic and anthropogenic pressures, which will aid policymakers and stakeholders in formulating strategies for drought preparedness and response.