Groundwater plays an important role in mitigating drought. It is necessary to analyze the spatiotemporal variation characteristics of groundwater and establish an appropriate assessment for the risk of drought for disaster prevention. This study developed a novel approach for the drought risk assessment system based on the Hilbert Huang Transform (HHT) method to understand the spatial distribution of the risk of drought in terms of groundwater. We analyzed drought vulnerability applying the HHT to analyze the variation characteristics of groundwater level spatiotemporally and the physical mechanism of groundwater factors to quantify groundwater sensitivity to the environment, and present the resilience of each region. Furthermore, the drought hazard was determined using the standardized precipitation index and the dynamic drought intensity gave the durability characteristics of each region. The drought exposure was also investigated, which quantifies the water demand to satisfy people’s livelihoods for a certain population density. Based on the framework proposed in this study, an overall risk map of droughts in the Pingtung Plain was obtained. This study effectively classified the main time–frequency characteristics, the availability of groundwater, and the risk of drought in each region. A total of 11 of the 45 groundwater monitoring stations are located at the highest risk of level 5, most of which are located in the coastal area of Gaoping River and Linbian River. Over-pumping should be avoided in these areas. On the contrary, the alluvial fan area showed the lowest groundwater risk of drought. The results can be adopted for water management, drought resilience, sustainable development of groundwater resources, and decision making in determining drought risk.