The Intervention-Autonomous Vehicle (I-AUV) as the effective operation equipment in the deep sea is suppressed to the external and physical constraints, which makes it challenging to achieve underwater missions. Aiming at the trajectory tracking control of I-AUV with input saturation and output constraints, a higher-order control barrier function-quadratic program (HoCBF-QP) based control scheme is proposed in this paper considering the uncertainties, disturbance and dynamic interaction. Firstly, a robust adaptive control is presented to track the desired trajectory in a finite time, where a feedback control term, based on the continuous terminal sliding mode (TSM) technique, is designed to improve the tracking performance under the uncertainties, disturbance and dynamic interaction. Secondly, a time-varying HoCBF is further developed to handle the high relative degree time-varying output constraints, then the multiple high-order control barrier functions can bring a family of safety-critical control input to preserve the reachability of AUV posture and joints motion. Thirdly, a convex quadratic program (QP)-based separation control frame is designed to conduct the tracking problem and output satisfaction separately. Due to its globally optimal advantage, the proposed control design provides a flexible frame to track objectives for the constrained I-AUV systems. Comparable simulation results demonstrate the fast convergence, robustness and high tracking accuracy of the proposed HoCBF-QP control for I-AUV systems with constraints.