Understanding the interaction among water resources, social economy and eco-environment (WSE) is essential to achieving sustainable development goals (SDGs) in water-deficient regions. Therefore, an investigation of the relationship among WSE was carried out in Xinjiang Uygur Autonomous Region (Xinjiang), China's largest arid region. We propose a multi-dimensional relationship assessment framework, MRR, to study the relationship among WSE. The MRR framework consists of three main components: mechanistic analysis, relationship of indicators and relationship of subsystems. Based on MRR, the relationship among indicators and indicators selection are cleverly combined, eliminating duplicated information in indicator system; the innovative coupled TOPSIS model and regression analysis provide a new idea for quantitative calculation of complex system relationships. This multi-dimensional study from indicator relationship to subsystem relationship achieves a systematic evaluation of the WSE relationship. The results reveal that: (1) In Xinjiang, eco-environment is strongly related to the water resources and social economy, with typical correlation coefficients greater than 0.85. (2) For the whole region of Xinjiang, the increase in social economy is accompanied by deterioration in the ecoenvironment. Over the decades, for every 0.10 unit increase in the social economy score, the eco-environment score decreased by 0.0405. However, for every 0.10 unit increase in the water resources score, the ecoenvironment score increased by 0.0456. (3) For the regional cities, social economic growth has been accompanied by environmental degradation in 35% of regions. These findings indicate that the economic development in Xinjiang is unhealthy and need to focus on environment protection. Furthermore, the new framework is suitable for examining relationships among WSE and guide SDGs.