This article proposed a novel event-triggered integral sliding-mode control (ISMC) strategy for nonlinear system with disturbances via robust adaptive dynamic programming (ADP) considering control constrains. A mixed event-triggered ISMC scheme with two different trigger parts is developed and the optimal performance of sliding-mode dynamics with input constrains is ensured. By guaranteeing that the system trajectory converges to the sliding-mode surface with removing the input disturbances, a discontinuous part triggering rule is presented together with the existence analysis of a lower trigger interval time bound. Then, the optimal event-triggered control of sliding-mode dynamics is converted into a discounted factor-based $H_{\infty }$ constrained control problem under continuous part triggering condition. To solve the event-triggered HJI equation, a critic-only neural network (NN)-based ADP scheme is developed by applying a concurrent learning. The NN weight is updated by analyzing the uniformly ultimately bounded (UUB) stability of sliding-mode dynamics considering the event-triggered condition via the Lyapunov technique. Finally, the validity of our control strategy is verified by simulation.