Water scarcity is the major limiting factor to crop production in the hilly and gully Loess Plateau of central Gansu. A better understanding of the response of crops to the intensity and timing of water stress at different growth stages is helpful for optimizing agricultural production management systems under water-limited conditions. Based on the field experiment at Anding District, Dingxi City, the suitability of the Agricultural Production System Simulator (APSIM) model for simulating spring wheat yield, yield composition, and changes in soil water content under water stress, quantifying the effects of intensity and timing of water stress on yield, water consumption, and water use efficiency (WUE) in spring wheat, and identifying the most sensitive stage of spring wheat to water stress was verified. The results showed that the root mean square error values of the grain numbers, 1000-grain weight, yield, and soil water content of the APSIM model were less than 252.31 number/m2, 1.55 g, 170.26 kg/ha, and 1.73%, respectively. The normalized root mean square error values were less than 6.49, 5.92, 6.03, and 13.78%, respectively. The model effectiveness index values were higher than 0.64, 0.51, 0.52, and 0.50, respectively. The APSIM model had good adaptability to water stress in the study area. Further, the jointing stage was the most sensitive growth period for the water deficit of spring wheat in the study area, and this growth period had the greatest impact on spring wheat yield due to drought. The yield showed a trend of first increasing and then decreasing as irrigation increased. When the irrigation amount reached 300 mm, it reached a maximum value of 4866.19 kg/ha. Notably, WUE achieved a maximum value of 12.32 kg/ha with water stress at the tillering stage, followed by the emergence, jointing, heading, flowering, and grain filling stages. WUE showed a trend of first increasing and then decreasing as irrigation increased. When the irrigation amount reached 300 mm, it reached a maximum value of 15.03 kg/ha. Finally, the variations in yield and WUE with changed water consumption were not synchronous. WUE was at a maximum when irrigation was reduced in regions with severe water shortages, and the yield achieved a maximum with increasing irrigation in regions with relatively abundant water resources. In general, the jointing and grain filling stages were critical times for field irrigation management for spring wheat. Reasonable field irrigation management should be applied at these two growth stages to guarantee a higher yield and WUE of spring wheat in the hilly and gully Loess Plateau of central Gansu.