We performed a systematic analysis of the dynamic behavior of the cutting process of a machine tool with an unbalanced force induced by the mass eccentricity of the workpiece, a nonlinear cutting force, and a nonlinear suspension effect. Phase diagrams, power spectra, bifurcation diagrams, and a Poincaré section were applied to identify the dynamic motion. The simulation results show that nonperiodic dynamic responses are very prevalent in the cutting process of the machine tool. A stability analysis and modeling with multiple-degree-of-freedom coupling systems were also performed in this study. The results provide an understanding of the operating conditions under which undesirable dynamic motion takes place in this type of system and therefore serve as a useful reference for engineers designing and controlling such systems for precision manufacturing. Moreover, the results of this research will help clarify the dynamic characteristics of cutting machine tools and provide relevant and useful parameters to build or design better sensors.