This study investigates the trajectory-tracking control problem of a two-degree-of-freedom underwater manipulator operating in a complex disturbance environment. A dynamic model of the multi-link serial manipulator is first established. In this study, water resistance and additional mass forces acting on the manipulator are analyzed and calculated using differential analysis and the Morrison formula. To account for coupling between joints, the concept of equivalent gravity is introduced to precisely calculate the underwater manipulator’s buoyancy and gravity. As a result, a relatively accurate dynamic model of the underwater manipulator is established. To mitigate the influences of external disturbances and unmodeled parts on the manipulator, a finite-time extended state observer (FTESO) is designed to estimate system quantities that are difficult to measure directly. The robustness of the controller is enhanced using a feedforward compensation mechanism, and it is demonstrated that the observation error of the observer converges in finite time. Finally, a global fast terminal sliding mode controller (GFTSMC) is developed for trajectory tracking, integrated with the aforementioned observer, and designed to smooth and limit the controller’s output. The controller’s stability is proven using Lyapunov stability theory, and its effectiveness is verified through simulation-based comparison experiments.