The contact interaction mechanics of deformation broaching in low-plasticity materials is studied. Particular attention is paid to the study of the stress–strain state parameters and the plasticity margin in the deformation zone during the machining of gray cast iron EN-GJL-200. The stress–strain state was analyzed using a finite-element model of the deforming broaching process for each area of the deformation zone. The model parameters of the machined material were determined experimentally by compressing specimens of gray cast iron EN-GJL-200. The changes in the parameters of accumulated strain, stress tensor components, stress triaxiality ratio, hydrostatic stress, and plasticity margin at different deformation zones along the machined specimen depth are analyzed. It is shown that there is a zone of local plastic deformation in conditions of critical contact stresses. This leads to the appearance of tensile stresses that reduce the plasticity margin in the surface layer. The impact of tool geometry on the stress–strain state of the surface layer is also discussed, and recommendations for the optimal working angle of the deforming element are provided based on plasticity margin minimization.