Industrial applications of titanium alloys especially in aerospace, marine and offshore industries have grown significantly over the years primarily due to their high strength, light weight as well as good fatigue and corrosion-resistance properties. The machinability of these difficult-to-cut metallic materials with conventional turning (CT) techniques has seen a limited improvement over the years. Ultrasonically-assisted turnning (UAT) is an advanced machining process, which has shown to have specific advantages, especially in the machining of high-strength alloys. In this study a three-dimensional finite element model of ultrasonically-assisted oblique cutting of a Ti-based super-alloy is developed. The nonlinear temperature-sensitive material behaviour is incorporated in our numerical simulations based on results obtained with split-Hopkinson pressure bar tests. Various contact conditions are considered at the tool tip-workpiece interface to get an in-depth understanding of the mechanism influencing cutting parameters. The simulation results obtained are compared for both CT and UAT conditions to elucidate main deformation mechanisms responsible for the observed changes in the material’s responses to cutting techniques.