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Frequent drought events under climate change are endangering food security and sustainable agricultural development. Quantitative assessment of crop yield anomalies under drought conditions is essential for effective water resources management and adaptative drought risk mitigation strategies. In this study, a copula‐based bivariate probabilistic framework model is developed to assess the impacts of drought events on crop yield, where the correlation of crop yield anomalies and standardized precipitation evapotranspiration index (SPEI) at multi‐month lags are quantified. This model has advantages in quantifying the impacts of drought scales on crop yield through the joint probability of the corresponding series. Then, the model is applied to Xinjiang Province in Northwestern China, an arid region with extensive agricultural activities. SPEI and yield anomalies of wheat, maize and cotton during 1984–2015 are firstly identified, and then copula‐based framework is constructed to quantify probabilistic crop yield losses caused by drought events. Finally, crop water amounts and irrigation requirements under different drought severity conditions are compared and analysed. Our findings are: (a) wheat and maize yield anomalies are vulnerable to long drought time‐scales, with exceedance probabilities of required yield anomalies returning to normal are 19.3% for wheat and 21.1% for maize, while cotton is susceptible to short drought time‐scales, with exceedance probability of 42.3% for drought recovery; (b) response of wheat crop yield anomalies to the SPEI at 1‐, 3‐, 6‐ and 12‐month scales is the most sensitive, followed by maize, and cotton is the least; (c) under extreme drought conditions, the probability of cotton yield reduction is lower than that of wheat and maize. Results may enhance our understanding of the impacts of drought scales on crops during the growing season, thus providing general guidance for rational irrigation management of crops and incentives for irrigation to mitigate drought risk, ultimately promoting sustainable agricultural development. [ABSTRACT FROM AUTHOR]