Laser beam welding of copper (Cu) using near-infrared radiation is extremely challenging due to its high thermal conductivity and large laser reflectivity. In the present study, the challenges and benefits of using spatial beam oscillation during quasi-continuous wave (QCW) pulsed laser beam welding of 0.4 mm Cu to 1 mm Cu in lap joint configuration are presented. This work demonstrates how laser beam oscillating parameters can be used to control the laser weld quality and laser weld dimensions for Cu-Cu joining. Compared to a non-oscillated laser beam, welds made using laser beam oscillation showed fewer spatters, porosities, and better surface quality. Four levels of oscillating amplitudes (0.2 mm, 0.4 mm, 0.6 mm, and 0.8 mm) and oscillating frequencies (100 Hz, 200 Hz, 300 Hz, and 400 Hz) were compared to reveal the effect of beam oscillation parameters. The weld width was mainly controlled by oscillating amplitude, while weld penetration was affected by both oscillating amplitude and frequency. As the oscillating amplitude increased, the weld width increased while the weld penetration decreased. Increasing the oscillating frequency reduced the weld penetration but had a negligible effect on the weld width. The maximum tensile force of approximately 1944 N was achieved for the joint with a high width-to-depth ratio with an oscillating amplitude of 0.8 mm and an oscillating frequency of 200 Hz.