To avoid the actuator saturation caused by communication limitation in practical applications, based on the impulsive control strategy constrained by saturation characteristics, in this paper, we study the mean-square bipartite consensus for a class of leader-following multi-agent systems with randomly occurring uncertainties and randomly occurring nonlinearities. By using the Lyapunov stability theory, convex hull theory and algebraic graph theory, some sufficiency conditions for multi-agent systems to achieve mean-square bipartite consensus are given. Finally, a numerical simulation is provided to verify the effectiveness results.