As one of the effective market instruments in carbon emission reduction policy, carbon trading is capable of promoting the smooth implementation of the “dual carbon” goal. Based on the path evolutionary game method of information economics, this paper constructs a dynamic game model of the evolution and development of government and enterprise carbon emission reduction. It also analyzes the evolution and development law of government and enterprise carbon emission reduction. We used the carbon market trading data of Guangdong Province to simulate the evolutionary game path of government and enterprise carbon emission reduction under the “double carbon” target and then selected strategies. Results show that (1) Scientific adjustment of carbon quota can effectively shorten the realization time of carbon emission reduction probability of high-pollution enterprises, obtain additional surplus carbon quota, and win extra carbon emission reduction income; (2) Increasing financial subsidies can improve the probability of carbon emission reduction of high-pollution enterprises but cannot prevent the periodic change in carbon emission reduction probability, which in turn helps prolong the “window period” of government regulation on carbon emission reduction; (3) Increasing carbon emission penalties will help high-pollution enterprises actively reduce emissions and improve the motivation of government supervision; (4) The government can introduce a dynamic reward and punishment mechanism. If the government properly chooses the reward and punishment strategy, it may not necessarily pay additional subsidies, so that the government and enterprises can cooperate in tacit agreement to achieve the goal of carbon emission reduction; (5) If the price of carbon emission permits is adjusted, high-pollution enterprises will actively reduce carbon emissions and gain greater benefits no matter what regulatory measures the government takes. Results of this study have profound significance for carbon emission reduction strategies and government regulation of high-pollution enterprises and will help China achieve its “dual carbon” development goal.