The spine vertebral body is of multi-layer composite structure and is prone to thermal damage, so the surgical robot should accurately control its axial drilling force when drilling the bone tissue of the pedicle. However, the control precision of general-purpose force controllers is insufficient for surgical safety due to the individual differences among different persons and the rigid-soft coupling structure composed of spine and soft tissue. This paper aims to improve the accuracy of the axial drilling force control. Firstly, a rigid-soft coupling model of the spine-soft-tissue system is established based on mass, spring, and Maxwell viscoelastic element. Then, the model parameters are calibrated based on the measured force data from a stress relaxation experiment on the isolated sheep spine. The axial feed rate of the bone drilling is adjusted by a PID (proportional-integral-derivative) controller. And the controller parameters are tuned by the standard particle swarm algorithm with dynamic weights, based on the transfer function of the calibrated rigid-soft coupling model. Finally, the simulation proves that the closed-loop control system is of good dynamic performance and robustness. Results of the drilling force control experiment on the isolated sheep spine show that, the steady-state error of the step force response of the axial drilling force is less than 0.15 N, the relative force control error is less than 3%, and in fact without any noticeable overshoot. The sinusoidal force response amplitude is attenuated to -3 dB at a frequency of 3.49 rad/s, which means that the closed-loop control system has a wide enough control bandwidth. The force control accuracy and control bandwidth of the proposed method can meet the force tracking requirements of the surgical robot when performing bone drilling, and the safety of the automatic bone drilling process is improved.