As a social problem involving a wide range of objects, targeted poverty alleviation governance needs to clearly define stakeholders and identify their behaviour choices, so as to seek a multiagent collaborative governance strategy, and strive to jointly promote the realization of a targeted poverty alleviation goals in an atmosphere to win-win cooperation and benefit sharing. By constructing a three-subject evolutionary game model of local government, social organization, and poverty group in the process of targeted poverty alleviation, this paper discusses the influence of their behavioural decisions on multisubject collaborative governance of targeted poverty alleviation and selects samples to carry out simulation experiments on the model. The results show that, first, superior government support has little effect on the evolution of tripartite competition, and the conclusion is inconsistent with the general cognition. However, the enhancement of support from local governments and social organizations can effectively promote the transformation of the willingness of the poor groups to cooperate. Second, a modest increase in the punishment of social organizations and poor groups can have a binding effect on the behavioural strategy choices of both sides and ultimately promote the process of targeted poverty alleviation. Third, the increase in the benefits of social organizations and poor groups can significantly improve the willingness of both sides to cooperate, so the “endogenous driving force” of the poor groups should be enhanced to achieve the Pareto optimal state of targeted poverty alleviation.