Tracking control of an autonomous tethered underwater vehicle (ATUV) for a successful marine operation is a challenging task due to the complex and nonlinear dynamics of the vehicle characterized by parametric uncertainties. Besides these issues, the vehicle mainly operates in an uncertain and unpredictable environment. To deal with the ATUV control tracking problem, this article proposes a new tracking control approach that will be named saturation-based adaptive computed torque+ (SACT+). The proposed SACT+ is designed using a variable saturation function, a computed torque structure, a saturation-based dynamic feedback, and an adaptive mechanism. Then, several arguments, based on the well-known Lyapunov techniques, are proposed to prove the stability behavior of the final closed-loop dynamics. This ensures the convergence (theoretically) of the vehicle tracking error to the origin, leading to stable and safe operations. However, this tracking error (experimentally) only stays around the origin due to many factors, such as the measurement noise from the vehicle’s sensors, the inherent uncertainties of the vehicle combined with external disturbances from the marine environment, etc. Different tests are conducted in real-time using our underwater vehicle Leonard prototype to validate the proposed SACT+. The obtained experimental results show the effectiveness and robustness of the proposed SACT+ approach in real-life cases. Finally, the performance and energy consumption indices, as well as comparative experimental studies with two well-established controllers (from the literature), confirm the relevance of the proposed approach for controlling small-sized and/or low-cost underwater vehicles.