To eliminate or reduce stick–slip vibration in torsional vibration of the drilling string and improve the rate of penetration (ROP), a stick–slip vibration model of the drilling string considering the ROP was established based on the multidimensional torsional vibration model of the drilling string. The model was verified by simulation analysis. The characteristics of the drilling string stick–slip vibration in the three stages of stationary, slip, and stick were analyzed. This paper investigated the influence of rotary torque, rotary speed, and weight on bit (WOB) on stick–slip vibrations in the drill string. Based on this, the relationship between the drilling parameters and ROP was established. Drilling parameter optimization was completed for soft, medium-hard, and hard formations. Results showed that appropriately increasing torque and decreasing WOB can reduce or even eliminate stick–slip vibrations in the drill string and increase the ROP. The parameter optimization increased the ROP by 11.5% for the soft formation, 13.7% for the medium-hard formation, and 14.3% for the hard formation. The established drill string stick–slip vibration model provides theoretical guidance for optimizing drilling parameters in different formations.