Under the background of carbon neutrality, the steel industry, as the largest carbon emission body, faces the increasing pressure of carbon emission limitation. It is urgent to improve the production process and improve the proportion of clean production taking scrap steel as raw material. In this study, game theory and chaos theory are used to analyze the influence of carbon emission limiting pressure and scrap quality improvement on each game player in supply chain. The results show that carbon emission reduction encourages steel enterprises to develop scrap steelmaking. At the same time, the quality of scrap materials needs to be improved to meet the requirements of scrap suppliers and steel enterprises to achieve optimal profits. However, the improvement in the quality of scrap materials is not conducive to system stability. At present, iron ore is still the main raw material in the steel industry, and the transition to scrap steel should be gradual and smooth. Government department uses big data and other information technologies to strengthen the price supervision of the steel market, and guide firms to consciously comply with the market rules to adjust the price of raw materials, otherwise it may lead to the turmoil of the entire steel market, and even the trend of economic chaos to bankruptcy.