Tribological behavior of Cu is peculiar among soft metal when it rubs on diamond flat in experiments, and passivating element F and H at Cu/diamond interface can affect mechanical properties and even tribological characteristics as well, related special adhesive transfer (fracture location) and adhesion tuning mechanism at Cu/diamond interface remain obscure. Here, we investigate the interfacial structure change, electronic and mechanical properties of Cu/diamond and interface with fully F passivation (Cu/diamond:F) through first-principles calculations. The study shows that Cu(111)/diamond(111) interface exhibits the special phenomenon of adhesive transfer (different cleavage location and interfacial strength under applied load) due to adhesion, and this contribute to different frictional properties among soft metal. The effect on mechanical properties of F at Cu/diamond interface is studied systematically, passivation of fluorine on diamond surface reduces work of separation of the interface significantly, from 3.64 to 0.02 J/m². Combining with kinetic analysis, we gain that fluorine might be a kind of promising adhesion-reducing element at interface and improve related tribological characteristics of Cu(111)/diamond(111) system. The results of this study benefit the understanding of different tribological properties of Cu/diamond system, adhesion reduction mechanism of fluorine at interface and its effect on tribological behavior at atomic scale.