To enhance the autonomy of underwater operations in marine and ship engineering, this paper proposes a method for object grasping based on an MB-Grasp model. First, an RGB image of the target is captured by a binocular camera mounted on the operation platform, and a disparity depth map is generated using a semi-global stereo matching (SGM) algorithm. The RGB and depth images are then fed into the MB-Grasp network to estimate the target's position, category, and grasp angle. Subsequently, the target's pose in the robotic arm base coordinate system is derived through coordinate transformation. Path planning is performed using the rapidly-exploring random tree star (RRT*) algorithm, and inverse kinematics solves the joint angles for each path point. A smooth trajectory in joint space is generated via polynomial interpolation to drive the robotic arm to execute the grasp. An experimental platform simulating the underwater operation environment of a ship was constructed, and autonomous grasping of simulated cables and small components was successfully achieved. This study provides a feasible solution for autonomous underwater operations in ship underwater engineering.