Soft-bodied robotic manipulators have great potential for use in minimally invasive surgery, owing to their advantages of high flexibility with infinite degrees of freedom (DOF). One of the potential applications is to perform blood suctioning, which is inevitable during the surgery. To attain higher efficiency in suctioning, the robotic tip should remain vertical while moving along on the work surface. Motivated by this application, this paper presents a novel soft robot design and its control scheme to properly configure the tip of a two-segment soft robot while following a planned trajectory on the work surface. Aiming to reduce the incision size and the possibility of infection, a 3D-printed soft-bodied manipulator utilizing the cable-driven mechanism with a diameter of 9 mm was designed and fabricated. An additional DOF was added through a motorized insertion stage. The robot system was modeled using piecewise constant-curvature assumption, and an RGB-D vision was employed to enhance the accuracy of the kinematic-based controller. Performances of the tip positioning and verticalizing were evaluated via simulation, and further verified through experiments. The results confirm that the manipulator is capable of following different trajectories at various velocities while keeping its tip vertical. Compared to other similar works, our results are satisfactory with an RMSE of trajectory tracking within 7 mm, and a maximum angular deviation of 6. Fluid suction experiments were conducted to demonstrate its effectiveness for automated 3D suction. This work offers a new tool to support the surgeons for surgical blood suction.