Highlights: [•] Modeling of cutting forces while applying a slicing motion to the push-cutting process. [•] Analysis of state of stress at the cutting edge. [•] Stress Intensity Factors for cutting with a symmetrical and asymmetrical cutting knife. [•] Fracture toughness of the paper sheet material is determined through DENT test. [•] The new model is verified by sideways push-slice cutting stacked thin paper material. [Copyright &y& Elsevier]