Upon the implementation of the European Union Carbon Border Adjustment Mechanism (CBAM), substantial challenges are anticipated to impact the international trade of Chinese steel products. To safeguard the competitiveness of Chinese steel products on the global stage, this paper establishes a tripartite evolutionary game model, involving large steel enterprises, small- and medium-sized steel enterprises, and the government. The model integrates collaborative emission reduction and free-riding benefits among enterprises, along with the government’s dynamic subsidies and penalties. First, we calculate the replicator dynamic equations and conduct stability analysis to obtain the evolutionary trends and system equilibrium points in different phases of the CBAM. Then, we validate the evolutionary theoretical analysis of the model through example simulation analysis. Finally, we explore the impact of different parameters on the agents through a sensitivity analysis of parameters. The findings indicate that (1) large enterprises demonstrate greater sensitivity to CBAM, making their production structures more susceptible to changes in CBAM policies; (2) small- and medium-sized enterprises are more prone to free-riding behavior influence; (3) government intervention should be kept within appropriate boundaries, as excessive intervention may lead to strategic oscillation, with passive management being chosen by the government during the strengthening phase of CBAM; (4) elevating the price in the Chinese carbon market would slow down the structural changes in the production of Chinese steel enterprises, serving as an effective measure to counteract the impacts of CBAM. This paper provides theoretical support for how steel enterprises and the government can respond to CBAM, aiding stakeholders in selecting optimal strategies during different implementation stages and mitigating the impacts of the CBAM to the maximum extent possible.