The development of high-performance batteries and electronics requires advanced joining technologies for laminated metallic components. However, laser welding copper foil stacks remains complex due to the material’s extreme thermal conductivity and high reflectivity. These physical properties, combined with the mechanical instability of thin-film laminates, often lead to inconsistent penetration and significant thermal distortion during battery tab manufacturing. This study systematically investigates the welding of ten-layer stacks consisting of 50 µm Cu-ETP foils using green laser radiation (λ ≈ 515 nm). While conventional infrared lasers provoke unstable processes, the green wavelength provides a stable initial absorption, facilitating a controlled process window for deep penetration welding. The research compares continuous wave (CW) operation with two distinct pulsing strategies: Pulsed Stationary (PS) and Pulsed Constant Feed (PCF). To decode the correlation between melt pool behavior and the resulting joint properties, a combination of in-situ high-speed videography, optical profilometry, and Electron Backscatter Diffraction (EBSD) was employed. Results demonstrate that CW operation leads to significant heat accumulation as a direct consequence of the continuous energy input and the specific thermal response of the foil stack, resulting in pronounced "wavy" buckling. In contrast, pulsed strategies facilitate periodic thermal relaxation, which effectively stabilizes the vapor capillary and narrows the weld seam. Furthermore, EBSD analysis confirms that tailored pulsing promotes a refined, equiaxed solidification morphology, whereas CW welding results in coarse grain clusters. Overall, tailored pulsing strategies mitigate the thermal limitations of CW welding, ensuring superior process stability and geometric precision in conductive foil assemblies.