Field experiments were conducted under a rain proof shelter using 15 sweetpotato cultivars with well-watered and drought stress treatments. Leaf physiological characteristics of different sweetpotato cultivars under drought stress were studied. The results showed that the leaf area index of all varieties decreased in different degrees under drought stress, which evaluating the difference of drought tolerance in varieties. Cluster analysis of drought resistance coefficient revealed that 15 sweetpotato cultivars were classified into three drought resistant types. The drought-tolerant cultivars were Jishu 21, Jishu 25, Jixu 23, Jishu 15, and Yanshu 25. The moderate drought-tolerant cultivars were Xushu 18, Jishu 26, Beijing 553, Jizishu 2, and Jishu 18. The drought-sensitive cultivars were Zhengshu 20, Jizishu 3, Jishu 22, Jizishu 1, and Ayamaraski. The correlation analysis between leaf area index and drought resistance coefficient demonstrated that the drought-tolerant cultivars could maintain higher leaf area index under drought stress, while the leaf area index under well-watered could not reflect the drought resistance. Drought stress resulted in the decline of chlorophyll content, the relative water content of functional leaves, and the increase of relative electrical conductivity of functional leaves. Under drought stress, the chlorophyll content and relative water content of functional leaves were significantly positively correlated with drought resistance in different cultivars, while the relative electrical conductivity of functional leaves was significantly negatively correlated with the drought resistance of sweetpotato varieties. In summary, leaf area index, chlorophyll content, relative water content, and relative electrical conductivity of functional leaves could be used as comprehensive evaluation indexes for identifying drought resistance of sweetpotato cultivars.