This article studies the model-based event-triggered control (ETC) for the tracking activity of the underactuated surface vessel (USV). Following this ideology, the continuous acquisition of states is no longer needed, and the communication traffic is reduced in the channel of sensor to controller. The control laws are fabricated in the frame of an adaptive model, which is renewed with the states of the original system whenever the triggering condition is violated. In the scheme, both internal and external uncertainties are approximated by the neural networks (NNs). To decrease the computing complexity, the minimum learning parameters (MLPs) are involved both in the adaptive model and the derived controller. The adaptive laws of only two MLPs are devised, and their updating only happens at triggering instants. Using the MLPs, an adaptive triggering condition is further derived. To avoid the ``Zeno'' phenomenon in small tracking errors, a dead-zone operator is designed for the triggering condition. Furthermore, we incorporate the dynamic surface control (DSC) into the controller design, such that the jumping of virtual control laws at triggering instants is smoothed and the problem of ``complexity explosion'' is circumvented. Through the techniques of the impulsive dynamic system and the direct Lyapunov function, the parameter setting for the DSC is derived to guarantee the semiglobal uniformly ultimate boundedness (SGUUB) of all the error signals in the closed-loop system. Finally, the effectiveness of the proposed scheme is validated through the simulation.