This paper presents the development of a new stochastic approach to characterize random tool motion during machining. The complexity of cutting mechanism is represented by a random excitation system related to physical properties of the material being machined. A Markov-chain based stochastic approach is developed to model the random tool motion as the response of a machining system under the random excitation. In considering a turning operation, a concept of group distributions is introduced to characterize the global effect on the cutting force due to the variation of a certain material property. A model of segment excitation is used to describe its micro function within an individual revolution. A distribution pattern observed in the material property is represented by a transition model. The simulation of random tool motion during machining resembles the generation of Markov chains. Microstructure analysis and image process are used to collect data, calculate relevant statistics, and estimate the system parameters specified in the developed stochastic model. As illustrated in this paper, the developed stochastic model can be effectively used to simulate the random tool motion and to learn rich information on the performance measures of interest such as machining accuracy and finish quality. The new approach represents a major advance to create a fundamental scientific basis for the realization of a reliable and effective prediction system for information processing in sensor-based manufacturing.