The dynamics of a cutting process are very complex in nature. It involves not only the changes of plastic state in the intensive deformation zone but also the elastic behavior of work material surrounding the deformation zone, especially in the vicinity of the tool nose region. These changes are induced by the inner and outer modulations of the uncut chip thickness during the process and at the same time govern the variation of the cutting force. Based on these causal relationships, the transfer function between the vibration variables and the dynamic force components for a single degree-of-freedom machining system has been developed. The characterization of the mechanics of the cutting process by the new model provides more insight into the physics of the cutting dynamics. The model has been tested through computer simulation for both orthogonal wave-generating and wave-removing processes. By reference to existing experimental evidence, the theoretical predictions show a very good agreement with the test results.