In this paper, the Johnson-Cook constitutive model is modified by considering the influence of hard point such as TiC and NbC in the matrix of Inconel718 on the deformation stress. The theoretical model of cutting specific energy in the main deformation zone of Inconel718 is modified based on the new constitutive model by combining the strain gradient theory. The effect of different cutting parameters on cutting specific energy is studied, and the effect of cutting specific energy on cutting deformation and the resulting dimensional effect are also analyzed. The research results show that cutting specific energy increases with the increase of cutting speed. With the increase of cutting thickness, the cutting specific energy reduced, and the trend is non-linear. The change of undeformed chip thickness will cause size effect. The cutting specific energy increases with the reduction of the thickness of undeformed chip, and the impact of the thickness of undeformed chip on the cutting specific energy becomes smaller and smaller as the speed increases. The existence of hard points makes the main deformation zone generate a large amount of heat energy and deformation energy, which leads to dimensional effects and makes the material be more prone to adiabatic shear instability, then leads to the increase of cutting specific energy. With the increase of cutting specific energy, the width of adiabatic shear band is narrowed, the degree of serration is aggravated, and the chip morphology is closer to the experimental results.