This paper proposes a new framework for the autonomous underwater operation of underwater vehicle manipulator systems (UVMS), which is modular, standardized, and hierarchical. The framework consists of three subsystems: perception, navigation, and grasping. The perception module is based on an underwater stereo vision system, which provides effective environment and target information for the navigation and grasping modules. The navigation module is based on ORBSLAM and acoustic odometry, which generates the global map and plans a trajectory for the first initial stage. The grasping module generates the target grasping pose based on the extracted point cloud and the current robot state, and then executes the grasping task based on the motion planner. The proposed system is tested to perform several underwater target grasping tasks in a water tank, demonstrating the effectiveness of the system.