The main purpose of this work is to study the influence of copper content on Al–Si–Mg aluminum alloy’s (6351) machinability. This alloy’s machinability was evaluated through cutting tool torque and thrust force measurements, holes’ surface roughness, diameter, roundness, cylindricity and subsurface modifications during the reaming process. The Al–Si–Mg alloy samples were produced with five levels of copper (0.07%, 0.23%, 0.94%, 1.43% and 1.93%) and have a chemical composition of the other alloying elements practically constant within the recommended range by the Aluminum Association for this alloy. The main mechanical properties of the 6351 aluminum alloy samples were obtained by microstructural analysis and microhardness, hardness and tensile tests. Major amounts of copper resulted in a significant increase in microhardness, hardness and ultimate tensile strength of the aluminum alloy, while elongation after fracture decreased. A 23 factorial design was used to verify the effect of copper content and cutting parameters cutting speed and feed rate in machinability responses. Furthermore, it was developed an adjusted model to optimize the cutting parameters selection to machine the alloy with the best copper content for each response parameter of the reaming process. The results showed a significant influence of copper content in this aluminum alloy’s machinability. Lower values of torque and thrust forces, better surface finish, lower roundness and cylindricity deviation were obtained increasing copper content in Al–Si–Mg aluminum alloy (6351).