A model of the cutting process is formulated based on a random variation of the specific cutting resistance. The cutting resistance is generated as a one-dimensional univariate Gaussian process using the spectral representation method. The random responses are discussed and compared with the deterministic ones within the ranges of parameters where chaotic motion occurs. Contrary to a claim for continuous systems, in which the variance of the noise dampens the chaotic vibration, such a behavior is not observed in the discontinuous system. The chaotic response is still present and the stochasticity induces immense impact forces during the transient period.