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The street protests and other mass demonstrations that have occurred frequently in recent years have resulted in considerable political pressure and have destabilized countries. How governments respond to such emergencies, and whether to evacuate protesters quickly, has been one of the most important public management challenges facing modern governments. In the case of evacuating protesters through police force, issues to consider include the cognitive differences among the conflicting parties and the cost-benefit considerations between the alternative strategies of mandatory evacuation and compromise. In this paper, the evolutionary dynamic of the mandatory evacuation of protesters by police is analyzed by extensive evolutionary game theory. Considering the cognitive differences among the conflicting parties, mental models of the interactions between government officials and protesters are constructed, which can not only avoid the uncertainty of evolutionary equilibrium but also consider the belief learning in the interior of the dynamic stage game. The evolutionary dynamic analysis of the mandatory evacuation of protesters is subsequently performed. To verify the effectiveness of the model set out, a multiagent simulation analysis based on a real case study of the Ningbo PX incident is presented. Furthermore, the decision-making related to police evacuation of protesters is based on the cost-benefit analysis between mandatory evacuation and compromise, the minimal number of police required, and the on-the-spot deployment plans of the police. The analysis shows that when facing protesters marching along a street, the evacuation measures are more effective if the police actions target the first several rows of protesters. However, in the case of protesters gathering near iconic buildings (or surrounding their demonstration leaders), the emergency plan of the mandatory evacuation of the protesters is less effective.