With the increasing performance and appearance requirements of electronic products, higher standards have been put forward for the machining accuracy and quality of the precision copper electrode for product molds. The precision copper electrode is large in material plasticity and small in size. Burrs are easily generated during the cutting process, and subsequent cleaning is difficult. In this paper, according to the geometric features of the copper electrode, the distribution type and formation mechanism of burrs are deeply analyzed. The influence of cutting-edge geometry on burrs lateral dimension is investigated by simulation. Further, the new left-handed fillet milling cutter is designed that takes into account the simultaneous cutting of the end edge and the circumferential edge. Finally, based on the new milling cutter, burrs suppression machining process adapted to different geometric features is planned. Experiments show that the new cutter and process can greatly reduce the size of burrs and basically realize burrs-free machining compared with the conventional process of the ordinary right-handed milling cutter, and the service life of the new cutter is longer, which can meet the actual machining needs.