The increasingly severe phenomenon of groundwater drought poses a dual threat to the development and construction of a region, as well as its ecological environment. Traditional groundwater drought monitoring methods rely on observation wells, which makes it difficult to obtain dynamic drought information in areas with limited measurement data. Based on Gravity Recovery and Climate Experiment (GRACE) satellite technology and data, the suitability of the standardized groundwater index (GRACE_SGI) was explored for drought characterization in the Mu Us Sandy Land. Multiscale and seasonal trend changes in groundwater drought in the study area from 2002 to 2021 were comprehensively identified. Subsequently, the characteristics of hysteresis time between the GRACE_SGI and the standardized precipitation index (SPI) were clarified. The results show that (1) different fitting functions impact the parameterized GRACE_SGI fitting results. The Anderson–Darling method was used to find the best-fitting function for groundwater data in the study area: the Pearson III distribution. (2) The gain and loss characteristics of the GRACE_SGI are similar, showing downward trends at different time scales, including seasonal scales. (3) The absolute values based on the maximum correlation coefficients between the SPI and the GRACE_SGI at different time scales were 0.1296, 0.2483, 0.2427, and 0.5224, with time lags of 0, 0, 12, and 11 months, respectively. The vulnerability of semiarid ecosystems to hydroclimatic changes is highlighted by these findings, and a satellite-based framework for monitoring groundwater drought in data-scarce regions is provided.