Due to the lack of generality for the accurate prediction of material separation, the finite element simulation is not well-established for shear cutting processes. Usually, the detailed material-specific behavior is determined in experiments, which are used for calibrating the underlying fracture criterion mandatory for a reasonable simulation. Unfortunately, the parameter identification for advanced constitutive modeling approaches is pretty involved and hardly practicable for real-life applications. Therefore, this study explores the applicability and practicality of a basic but well-known failure criterion for the finite element analysis, where model parameters can quite easily be determined. The Johnson-Cook approach is applied for the simulation of shear cutting an aluminum alloy. The investigation shows that the adaptation of basic material-characterizing modeling for a problem-oriented failure behavior enables the prediction of the real process in sufficient precision.