Mechanical automatic vertical drilling tools provide the advantages of high temperature resistance, low cost, wide application range, etc.; however, since the deviation correction and deviation prevention are realized by the gravitational and mechanical structure, the working accuracy under the condition of stick-slip vibration is greatly affected. This paper, with introduction to the stick-slip vibration mechanism, summarizes its concrete influence factors, and compares the existing methods to limit stick-slip vibration at home and abroad to explore suitable stick-slip vibration suppression methods for the mechanical automatic vertical drilling tools so as to provide reliable technical support for improvement of deviation prevention and correction capability.