Machining in the scale of nanometer and investigating its behavior is premier in the field of machining. Molecular dynamics is a new robust tool to investigate controlling mechanisms in atomic scales, complex dislocation, and grain-boundary in severely deformed workpieces with the submicron dimensioning; consequently, process simulation was performed by molecular dynamics method. In this study, some useful parameters of tool geometry in orthogonal cutting of monocrystalline copper were investigated. With this end in view, relief angle, rake angle, and tooltip radius were considered as influential geometrical parameters of orthogonal cutting of monocrystalline copper. By using the Response Surface Method (RSM), the variation effect of input parameters was studied on the cutting output parameters like cutting force, temperature, and hydrostatic stress all in nanometer precision. Furthermore, with mathematical modeling using a second-order linear regression equation fitted to the process outputs, single objective and multi-objective optimization of the cutting process was followed.