Stick-slip phenomena in the oil and gas drilling sector cause drillstring vibrations that provide major issues. These vibrations result in reduced drilling efficiency, equipment malfunctions, and possible dangers. This work introduces a thorough method for modeling and regulating stick-slip behavior. It utilizes a mechanical model with three degrees of freedom (3-DOF) that incorporates the influence of dry friction. The model combines both axial and torsional degrees of freedom to precisely reflect the intricate dynamics of the drillstring. Additionally, a control technique is suggested to alleviate stick-slip vibrations. This strategy involves using a hybrid Proportional-Integral-Derivative (PID) controller that has been tuned using Genetic Algorithms (GA). The PID-GA controller is specifically engineered to manage the rotating speed, mitigate stick-slip oscillations, and improve drilling stability. The efficacy of the suggested 3-DOF model and PID-GA control method in reducing stick-slip vibrations during drilling is proven by numerical simulations conducted under different drilling situations. The findings demonstrate notable advancements in drilling performance, such as decreased vibrations caused by friction, improved efficiency in drilling, and extended lifespan of the drillstring. This research significantly helps to the progress of drilling operations by offering a strong framework for modeling and managing stick-slip behavior. As a result, it improves drilling performance and guarantees operational safety in the oil and gas industry.