Beech wood is a material commonly used for furniture, and cutting performance is the key to improving product quality and enterprise benefits. In this work, beech milling experiments using diamond cutters were carried out, and the changes in cutting power, temperature, and surface roughness were examined using the factor analysis method. The main results of this work are listed as follows: Firstly, a higher cutting speed and depth led to higher cutting power, temperature, and surface roughness. Meanwhile, cutting power and surface roughness were negatively related to the rake angle; however, cutting temperature first increased and then decreased with the increase in rake angle. Furthermore, cutting depth had greatest impact on the cutting power and surface roughness, followed by rake angle and cutting speed. Cutting speed had the greatest contribution to the cutting temperature, followed by cutting depth and rake angle. Only the cutting depth had a significant contribution to both cutting power, temperature, and surface roughness. Finally, optimal cutting parameters were determined to be a rake angle of 15°, cutting speed of 54 m/s, and depth of 0.5 mm. These values best meet the multiple objectives of lower cutting power, temperature, and surface roughness, which relate to superior product quality and enterprise benefits.