Spinal surgery is considered a high-risk surgery. To improve the accuracy, stability, and safety of such operations, we report the development of a novel six-degrees-of-freedom Robotic Spinal Surgical System that can assist surgeons in performing transpedicular surgery, one of the most common spinal surgeries. After optimization performed using Response Surface Methodology, the largest available workspace of the robot is determined and is found to easily cover the entire operation area. Cooperative control and navigation-based active control are implemented for different processes of the operation. We propose a hybrid control approach based on the speed and torque interface at the joint level. In this mode, the robot is compliant in Cartesian space, benefitting both the accuracy and efficiency of the operation. A comprehensive assessment index, combining the subjective and objective criteria in terms of positioning and operation efficiency, is proposed to compare the performance of cooperative control in speed mode, torque mode, and hybrid control mode. Active fine adjustment experiments are carried out to verify the positioning accuracy, and the results are found to satisfy the requirements of operation. As an application example, a pedicle screw insertion experiment is performed on a pig vertebral bone, demonstrating the effectiveness of our system.