Based on the perspective of conflict of interest between low-carbon ecology and economic and social development, this study explores the change mechanism of land use cover change (LUCC) and carbon storage (CS) in the context of “Dual-Carbon” goal and territorial spatial ecological governance, which is of great significance to optimize the construction path of “Dual-Carbon” goal and formulate low-carbon, ecological, high-quality, and sustainable economic and social policies in the urban areas. An integrated framework based on the System Dynamics model, the Patch Generation Land Simulation model, and the Integrated Valuation of Ecosystem Services and Trade-offs model was constructed to dynamically simulate the LUCC demand and CS of Wenzhou under four scenarios in 2035, and to analyze the spatial evolution mechanisms of LUCC and CS. The main results of the study show that in the Natural Development Scenario (NDS) and High-speed Urbanization Scenario (HUS), the expansion mechanism is similar, and the area of woodland decreases greatly, which is mainly caused by the rapid expansion of construction land and cultivated land. Under Low-carbon and High-quality Development Scenario (LHDS) and Ecological Safety Governance Scenario (ESGS), woodland and grassland increased significantly, mainly because low-carbon and ecological governance policies strengthened ecological land protection and limited construction land control. By 2035, the prediction results show that LHDS has the highest CS (2.231 × 105 kt), followed by ESGS (2.226 × 105 kt), NDS (2.191 × 105 kt), and HUS (2.142 × 105 kt). The range of increase and decrease was 0.189, −0.149, −1.676, −3.692%, and only in LHDS, CS increased by 42.05 kt. Therefore, in order to achieve the “Dual-Carbon” goal, Wenzhou needs to prioritize the combination of LHDS and ESGS to formulate relevant policies.