In order to solve the high-precision trajectory tracking control problem of teleoperation robot systems under complex working conditions-including actuator saturation constraints, dynamic uncertainties, asymmetric time-varying communication delays, and compound disturbances-a proportional-damping finite-time adaptive anti-saturation control strategy based on neural network compensation was proposed. Specifically, a proportional damping term was constructed using the position error between the master and slave ends to enhance the transient performance and robustness of the teleoperation system. Additionally, RBF (radial basis function) neural network was employed to approximate the system dynamic uncertainties and unknown gravity torques in real time. To tackle the actuator saturation nonlinear constraint issue, a finite-time anti-saturation control architecture was developed, which integrates a gain-adaptive switching mechanism and RBF neural network-based online dynamic compensation. This architecture achieves finite-time compensation for saturation dynamics and ensures smooth transitions of the execution torque. Furthermore, by incorporating a terminal sliding mode term, a finite-time adaptive controller was designed. Based on finite-time convergence theory, a parameter adaptive update law was formulated to guarantee that the estimation error converges to zero within a finite time. The boundedness and finite-time stability of the closed-loop teleoperation system under the proposed control strategy are rigorously proven using the multiple Lyapunov function method. Finally, comprehensive simulation experiments were conducted, and the results were compared with those of alternative control methods, which demonstrates the effectiveness and superiority of the proposed scheme. In studies involving complex and hazardous operations such as underwater pipeline welding, this technology overcomes constraints and enables the completion of high-precision welding tasks.This study overcomes the constraints in complex and hazardous operations such as underwater pipeline welding, enabling the completion of high-precision welding tasks.