Forests in water source areas are important factors for water supply security, soil, and water conservation, and their water consumption from transpiration is strongly affected by site conditions, including the slope aspect. However, the lack of research on how the slope aspect interferes with the response of stand transpiration to drought has hindered researchers from developing climate-resilient forest–water coordinated, sustainable development plans for different stand conditions. This study was conducted on Quercus wutaishansea forests in the southern part of Liupan Mountain in northwest China, and two sample plots were built on sunny and shady slopes. The responses of stand transpiration to various soil moisture and meteorological conditions on different slope orientations were analyzed. The results showed better-growing stands on shady slopes transpired more and consumed more soil moisture than those on sunny slopes. The soil moisture on shady slopes decreased rapidly below the threshold level during the drought, leading to a limitation of stand transpiration; however, its transpiration recovered rapidly after the drought. In contrast, stand transpiration on sunny slopes was not affected by this drought and maintained its pre-drought rate. Our results suggested that stands with higher water demand on shady slopes were more susceptible to drought when it occurred. This indicated that in the case of frequent droughts, the vegetation should be managed according to the vegetation-carrying capacities resulting from different site conditions.