In this work, the break-up dynamics of a single, Newtonian droplet dispersed in an immiscible Newtonian matrix undergoing a controlled mixture of shear and extensional flow is investigated using a homemade eccentric cylinder device. Hereto, different representative supercritical flows with varying shear/elongation balance have been applied. The effect of viscosity ratio is explored using droplets with a viscosity ratio of 0.1 and 1.3, respectively. In all cases, break-up is observed to proceed through an "end-pinching" mechanism. The experimentally obtained break-up times have been compared with scaling relations known from literature for simple shear and purely extensional flow. It is found that the global break-up dynamics is still shear dominated, even for conditions where the elongational contribution comprises a substantial amount (up to 30% on average) of the mixed flow.