Performing surgical tasks safely and reliably presents significant challenges, including obstacle avoidance, joint limit constraints, and motion smoothness during the tool-target alignment (T-TA) stage, as well as precise tracking of preoperative plans during the execution of the preoperative planning surgery path (EPSP). The traditional inverse kinematics methods fall short in addressing these complex motion planning and control issues within the unstructured and time-varying surgical environment. Therefore, a novel spatial-temporal varying primal-dual neural network (STV-PDNN) that incorporates guided obstacle avoidance and null space optimization to address spatial-temporal constraints during surgery is proposed. Firstly, a velocity control quadratic programming (QP) framework based on target distance and orientation metrics is constructed by considering the relationships among the surgical robot, the environment, and the surgical target. Then, the STV-PDNN enables real-time problem-solving across two specific stages, employing velocity vector projection for obstacle avoidance and joint space obstacle avoidance velocity superposition to enhance the obstacle avoidance guidance. Furthermore, the joint null space optimization and maximum manipulability, along with a preoperative planning path velocity feed-forward and feedback velocity control mechanism, are integrated into the STV-PDNN structure. The improvement facilitates smoother, lower-energy joint movements and effective motion singularity avoidance during the T-TA stage, as well as precise motion control in the EPSP stage. The experiments conducted on the redundant robot Diana7 Med validate the effectiveness of the proposed method in autonomously executing T-TA and EPSP for pedicle screw implantation, offering a promising solution for the task autonomy of surgical robot.