The integration of acoustic wave micromixing with microfluidic systems holds great potential for applications in biomedicine and lab-on-a-chip technologies. Polymers such as cyclic olefin copolymer (COC) are increasingly utilized in microfluidic applications due to its unique properties, low cost, and versatile fabrication methods, and incorporating them into acoustofluidics significantly expands their potential applications. In this work, for the first time, we demonstrated the integration of polymer microfluidics with acoustic micromixing utilizing oscillating sharp edge structures to homogenize flowing fluids. The sharp edge mixing platform was entirely composed of COC fabricated in a COC-hydrocarbon solvent swelling based microfabrication process. As an electrical signal is applied to a piezoelectric transducer bonded to the micromixer, the sharp edges start to oscillate generating vortices at its tip, mixing the fluids. A 2D numerical model was implemented to determine the optimum microchannel dimensions for experimental mixing assessment. The system was shown to successfully mix fluids at flow rates up to 150 µL/h and has a modest effect even at the highest tested flow rate of 600 µL/h. The utility of the fabricated sharp edge micromixer was demonstrated by the synthesis of nanoscale liposomes.