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By means of game theory, the effect of compassion mechanism on the evacuation dynamics of pedestrians from a room is studied based on a cellular automaton model. Pedestrians can choose to cooperate or defect in a snowdrift game during the movement. With the compassion mechanism, pedestrians share their payoff to the poorest peer when several pedestrians compete for the same empty cell. Simulation results show that the escape time grows with fear degree r of the snowdrift game, and the compassion mechanism will have a different effect on the system compared with the situation of a spatial game with fixed population. By payoff redistribution, the compassion can help the minor strategy to survive. When the fear degree r is large, the compassion can sustain the cooperative behavior, and spontaneously decreases the escape time. When the fear degree r is small, the compassion will decrease the cooperation frequency, and slightly increase the escape time. The phenomenon is explained by the evolution and competition of defectors and cooperators in the system. Finally, the effect of initial cooperator proportion, the effect of two exits, and the effect of"Richest-Following"strategy, and the effect of initial density are also discussed.