Stirred bioreactors are commonly used unit operations in the pharmaceutical industry. In this study, computational fluid dynamics (CFD) was used in order to analyze the influence of the impeller configuration (Segment–Segment and Segment–Rushton impeller configurations) and the impeller rotational speed (an operational parameter) on the hydrodynamic behaviour and mixing performance of a bioreactor equipped with a double impeller. A relatively close agreement between the power values obtained from the CFD model and those measured experimentally was observed. Various parameters such as velocity profiles, stress generated by impellers due to the turbulence and velocity gradient, flow number, and mixing time were used to compare the CFD simulations. It was observed that the impeller’s RPM could change the intensity of the interaction between the impellers when a Segment–Rushton impeller was used. In general, increasing the RPM led to an increase in total power and the stress acting on the cells and to a shorter mixing time. At a constant RPM, the Segment–Rushton impeller configuration had higher total power and stress acting on cells compared to the Segment–Segment impeller configuration. At lower RPM values (i.e., 50 and 100), the Segment–Segment impeller provided a shorter mixing time. Conversely, at the highest RPM (i.e., 150) the Segment–Rushton impeller had a shorter mixing time compared to the Segment–Segment impeller; this was attributed to the high level of turbulence generated with the former impeller configuration at high RPM.