A new technique for additive manufacturing was recently presented by depositing droplets as a continuous track on a substrate, where the droplets were ejected from laser remote fusion cutting of a metal sheet. For the here presented approach, the droplets are instead ejected from the sheet edge, termed the machining mode, which is compared to cutting. Here, the transmitted part of the laser beam does not hit and interact with the deposited track because of lateral dislocation. High speed imaging has shown that laser-induced boiling, which drives the melt downwards, causes asymmetric conditions in the machining mode by lateral pushing of the generated drop jet under the sheet, where the melt can even attach. Compared to machining, the cutting mode keeps less deviation of the drop trajectories, higher precision, and a smoother surface finish. It was demonstrated that the edge conditions after machining are sufficient to repeat the process. This enables additional technique opportunities, including recycling of a whole sheet of waste metal. By the aid of high speed imaging from two different perspectives, the melt flow behavior, the drop jet precision, and process trends with respect to parameters, drop ejection, and deposition were studied.