Cooperation and self-organized criticality are two main keywords in current studies of evolution. We propose a generalized Bak-Sneppen model and provide a natural mechanism which accounts for both phenomena simultaneously. We use the prisoner’s dilemma games to mimic the interactions among the members in the population. Each member is identified by its cooperation probability, and its fitness is given by the payoffs from neighbors. The least fit member with the minimum payoff is replaced by a new member with a random cooperation probability. When the neighbors of the least fit one are also replaced with a non-zero probability, a strong cooperation emerges. The Bak-Sneppen process builds a self-organized structure so that the cooperation can emerge even in the parameter region where a uniform or random population decreases the number of cooperators. The emergence of cooperation is due to the same dynamical correlation that leads to self-organized criticality in replacement activities.