Critical leaf nutrient concentrations have often been used to diagnose the nutritional status of crops. Determining critical leaf potassium (K) concentrations for the maximum root dry matter (RDM) will provide a reliable means of linking leaf K nutrient concentrations to the yield of sweet potato. Three field experiments, using varying K application rates (0–300 kg K ha−1) and two sweet potato cultivars, were performed in the Zhejiang Province of China. A new critical leaf K curve (Kleaf) based on the maximum RDM was determined to assess K nutrition in sweet potato and described by the equation Kleaf=4.55×RDMmax-0.075. A critical root K curve (Kroot) based on the maximum RDM was also determined to assess K nutrition and described by the equation Kroot=2.36×RDMmax-0.087. The K nutrition index (KNI) was constructed to identify the situations of K-limiting and non-K-limiting treatments. The leaf KNI (KNIleaf) ranged from 0.56 to 1.17, and the root K KNI (KNIroot) ranged from 0.52 to 1.35 during the growth period of sweet potato. The results showed that the critical leaf K concentration curve can be used as an accurate leaf K status diagnostic tool at critical growth stages that connected leaf nutrient concentration and sweet potato tuber yield. This K curve will contribute to K management of sweet potato during its growth period in China.