The effect of various beam offsets on the microstructure and the properties of welded joints was studied using optical microscope, scanning electron microscope, and energy dispersive spectrometer, combined with tensile and hardness tests to investigate the challenges caused by large differences in physical properties and poor metallurgical compatibility in the laser welding of dissimilar materials such as copper/stainless steel. The results show that the weld is semi-hourglass shaped under the influence of an evaporation force and Marangoni convection effect. When the beam is biased towards the copper side, the iron-rich phase disperses in the weld due to the liquid phase separation, resulting in an uneven distribution of the weld composition and hardness. In addition, the more copper content in the deposited metal, the lower the joint strength. When the beam is biased towards the steel side, the microstructure of the weld is austenite with a copper-rich phase, and the strength of the welded joint increases. Moreover, the maximum tensile strength can reach 240 MPa, equivalent to the copper base metal. Therefore, the best comprehensive performance of the welding joint can be obtained when the beam offset is -0.4 mm.