Advances in the machining of titanium work pieces are of particular interest to areas such as the aerospace and naval industry. However, titanium is known to be a difficult-to-machine material. Recent studies suggest that the presence of oxygen from ambient air has a significant influence on its wear mechanism. Removing oxygen from the system reduces tool wear and therefore improves the surface finish of the tool in the long term. However, the exact mechanism of wear caused by oxygen is still up to debate. In this work, we study molecular dynamics simulations of the cutting process of single crystalline hcp titanium on the (0001) plane with and without an oxide layer. Reference simulations with pure titanium of different crystal sizes are performed in order to reveal size effects. We find that the oxygen layer behaves very brittle compared to the bulk crystal material and influences the chip formation on the nanoscale. Instead of forming a smooth chip, as for pure titanium, the simulation with an oxide layer shows no chip formation at all in the observed time scale. The layer breaks and locally induces high temperatures of 1700 K in the material. These high temperatures could lead to enhanced interdiffusion of work piece and tool material and could therefore amplify the predominant tool wear mechanism.