In this study, we use the critical slowing down (CSD) theory to identify the precursory anomalies of groundwater radon based on the 1000-day continuous data from 8 monitoring stations in Yunnan Province, China during the seismically active period of 1993–1996. The low-frequency and high-frequency information were extracted from raw groundwater radon data to calculate their one-step lag autocorrelation (AR-1) and variance, respectively, in order to identify the precursory anomalies. The results show that the anomaly characteristics can be divided into three categories: sudden jump anomalies, persistent anomalies, and fluctuation anomalies. The highest average seismic recognition rate is 72.78%, based on the high-frequency information’s autocorrelation, while the lowest is 45.08%, based on the low-frequency information’s variance. The crustal activity and the change in hydrogeological conditions are possibly the main factors influencing groundwater radon anomalies in the selected period in the study area. There is a positive correlation between the anomaly occurrence time and epicentral distance when epicentral distance is less than 300 km, which may be related to the seismogenic modes and hydrogeological conditions. This study provides a reference for identifying groundwater radon anomalies before earthquakes by mathematical methods.