With global warming continuously worsening drought hazards, the Fuhe River Basin urgently requires insight into drought evolution laws to support resilient water resources management. However, traditional univariate indices such as the Standardized Precipitation Index (SPI) and Standardized Soil Moisture Index (SSI) are limited by their inability to capture the coupled meteorological-agricultural drought process and the time-lag effects between precipitation and soil moisture response. Therefore, a multivariate drought index—which integrates both precipitation and soil moisture information—is needed as a core tool for drought early warning and precise regulation. In this study, the calibrated SWAT model was used to simulate monthly soil moisture content in the Fuhe River Basin over the past 60 years. On a 3-month time scale, a Multivariate Standardized Drought Index (MSDI) was established by coupling the Standardized Precipitation Index (SPI) and Standardized Soil Moisture Index (SSI) using the Copula function. The main findings are as follows: (1) The Nash–Sutcliffe efficiency coefficient (NS) of the SWAT (Soil and Water Assessment Tool) model during the validation period reached above 0.70, indicating favorable performance in monthly runoff simulation. (2) The MSDI revealed frequent drought events in two periods, namely 1960–1979 and 2000–2019, demonstrating the periodic fluctuation pattern of droughts in the basin. (3) Wavelet analysis showed that compared with the previous two periods, the frequency of droughts in the basin increased significantly after 2000, with weakened periodic characteristics, intensified extreme drought events, and a further rise in drought risks. This study deepens the understanding of drought dynamics in the Fuhe River Basin and provides a scientific basis for regional sustainable water resource management and the formulation of climate adaptation strategies.