The critical factors that affect bottomhole stick–slip vibrations during vertical drilling operations are thoroughly investigated and analyzed in this research. Influential factors, such as rotation speed, weight on bit (WOB), bottom hole assembly (BHA) configuration, and formation properties, were studied in order to understand their part in the stick–slip phenomena. The analysis is based on a thorough review of previous research conducted on stick–slip drilling vibrations. A mathematical model was created that not only explains axial vibrations but also includes the torsional vibrations present in stick–slip occurrences, which helps with understanding the stick–slip phenomena better. This model can be used as an analytical tool to predict and evaluate the behavior of drilling systems under various operational circumstances. Furthermore, two drilling tests using a WellScan simulator were performed to validate the research findings and assess mitigation techniques’ viability. These test scenarios reflect the stick–slip vibration-producing situations, allowing us to test mitigation strategies. The finding of this study shows the effectiveness of two tactics for reducing stick–slip vibrations. First was the reduction of WOB, which successfully lowered the occurrence of stick–slip vibrations. The second was the increase in the rotation speed, which helped to control the stick–slip problem and increased the drilling speed. This study explains the complex dynamics of stick–slip vibrations during vertical drilling and offers practical, tried-and-true methods for reducing their adverse effects on drilling operations.