Reducing agricultural emissions and promoting carbon sequestration are vital for China to achieve its dual carbon goals. Achieving the green transformation of agricultural watersheds requires a thorough understanding of the internal transmission relationships within the watersheds and the underlying spatial correlation structures. This paper used the SBM-3E model to calculate the agricultural ecological efficiency of 17 prefecture-level cities in the Hanjiang River Basin (HRB) from 2010 to 2020, taking agricultural carbon emissions and a comprehensive non-point source pollution index as the unexpected output. The Gravity model and social network analysis methods were used to analyze the evolution characteristics of the network structure of agricultural ecological efficiency, and the secondary assignment procedure method was used to identify the driving factors from the planting structure, water use structure, and resource endowment. First, from 2010 to 2020, the overall agricultural ecological efficiency in the HRB demonstrates a declining trend, with efficiency values of 12.15, 9.40, and 6.67 in the upper, middle, and lower reaches, respectively. Second, the spatial correlation network density of agricultural ecological efficiency in the HRB is 0.17, with a network efficiency of 0.89. The correlation among units within the basin is relatively low, but stability is high. Moreover, the individual network spillover absorption capacity exhibits heterogeneity, and the status of each subject within the watershed follows a “core-edge” structure. Third, total water consumption and corn cultivation have a positive impact on the agricultural ecological efficiency network in the HRB, whereas agricultural water use and rice cultivation negatively influence the network. We propose policy recommendations to facilitate the advancement of green development in China’s agricultural watersheds and the achievement of the dual carbon goals.