The article presents the results of modeling free orthogonal cutting of a unidirectional aluminum matrix steel fiber composite using SPG method. During mechanical machining of such composites, various problems with the quality of the processed surface arise. Fiber layering, an increase in the surface roughness and other defects are observed. The SPG numerical method allows modeling the cutting of such materials and investigating the influence of the tool geometry, cutting speed, and feed on the quality of the processed surface. In this article, cutting of a fragment of a composite with two fibers is modeled and the dependence of the cutting forces on the processing speed is determined. The modeling results show that the SPG method can be successfully used to model the cutting of such a composites. Unlike traditional numerical methods, such as the finite element method, the SPG method made it possible to model such a phenomenon as the elastic springback of fibers immediately after passing the tool. The effect of the rake angle of the cutting tool on the degree of fiber layering was also studied. It was found that the degree of layering nonlinearly depends on this parameter.