In line with the Paris Agreement’s global carbon reduction targets, the rise of Carbon Capture, Utilization, and Storage (CCUS) technology offers significant opportunities to mitigate climate change. With the introduction of the Capacity Bidding Program (CBP), addressing the issues of insufficient power load adjustment flexibility and high CO2 emissions in energy-intensive industrial manufacturing during grid emergencies becomes essential. A low-carbon flexible manufacturing dispatch model that incorporates CCUS infrastructure is proposed. Firstly, distributed carbon capture power plants are introduced in industrial parks to reduce industrial enterprises’ dependence on the main grid. Secondly, the model considers the Capacity Bidding Program. Based on this, a low-carbon scheduling model aimed at maximizing the total manufacturer’s profit is constructed. The model includes raw material costs, power costs, carbon costs, and so on, and it can automatically determine the best load curtailment offers for the Capacity Bidding Program. The effectiveness of the proposed method in improving factory profit, maintaining grid stability, and reducing carbon dioxide emissions is verified through a case study of high-capacity lithium battery manufacturing.