Aiming at the difficult problem of regulating the mechanical properties of the machined surface in the dry cutting of aviation aluminum alloy 7075, and the deviation of the solution caused by the idealized assumption of stress-strain in the shear zone in the previous cutting models, the effect of cutting parameters on the average width of the shear zone and stress-strain behavior of aviation aluminum alloy 7075-T651 in the dry turning process, and the effect of strain-hardening behavior on the cutting model were studied based on the Oxley-Welsh theory. In addition, relationship models between shear flow stress and hydrostatic stress in cutting zone, hydrostatic-shear difference of material unit, microhardness of machined surface, as well as surface roughness were established, which reasonably explains the size effect and strain-hardening effect in the shear zone of workpiece material during dry turning of 7075-T651 aluminum alloy. The results showed that the slope K of the relationship model between shear flow stress and hydrostatic stress is the result of the combined effect of the size effect and the strain-hardening effect in the shear zone of workpiece material. When the 7075-T651 aluminum alloy is produced under the cutting conditions of cutting velocity vc = 240 m/min, feed rate f = 0.05 mm/r, and cutting depth ap = 0.15 mm, the machined workpiece had the best uniform plastic deformation, relatively highest surface hardness, up to 174.1 HV, relatively best surface quality, with roughness up to 0.78 μm, and relatively strongest load-bearing capacity in the service process.