Droughts are long-term natural disasters and encompass many unknown factors. Herein, yearly and seasonal standardized precipitation evapotranspiration index (SPEI) values were calculated by analyzing monthly temperature and precipitation data from 1971 to 2020. A cloud model was employed to obtain the spatiotemporal variations in the yearly distribution of drought weather. The cross-wavelet transform results revealed the relationship between the SPEI and atmospheric circulations. The results indicated that the average reduction rates of the SPEI-3 and SPEI-12 in Yinshanbeilu were 0.091 and 0.065 yr−1, respectively, and the annual drought occurrence frequency reached 30.37%. The annual station ratio and drought intensity showed increasing trends, whereas the degree of drought slightly decreased. The overall drought conditions indicated an increasing trend, the entropy (En) and hyper entropy (He) values demonstrated increasing trends, and the expectation (Ex) showed a downward trend. The fuzziness and randomness of the drought distribution were relatively low, and the certainty of drought was relatively easy to measure. The variation in the drought distribution was relatively low. There were resonance cycles between the SPEI and various teleconnection factors. The Pacific Decadal Oscillation (PDO) and the El Niño–Southern Oscillation (ENSO) exhibited greater resonance interactions with the SPEI than did other teleconnection factors. The cloud model exhibits satisfactory application prospects in Yinshanbeilu and provides a systematic basis for early warning, prevention, and reduction in drought disasters in this region.