Wire and arc additive manufacturing (WAAM) produces thin-walled parts superior to other additive manufacturing methods, because of its high efficiency, good compactability, and low cost. However, the WAAM accuracy is limited by its large heat input. Here, 0.8 mm 316L stainless steel welding wire is deposited via speed cold welding to form 30-layered thin-walled samples, with 2 mm thickness, and up to 65 mm height. The effects of three process parameters (the bottom current mode, scanning speed, and cooling time) on the deposition process stability, macro morphology, structure, and mechanical properties are studied. In the experiment, the probability density curves of electrical parameters of sample #GRBC-30 cm/min-10 s on the third and tenth layers were narrower than other samples, which implied a more stable process. The three process parameters mainly affect the deposition morphology and have a minor performance effect. The hardness and tensile properties mainly depend on the deposition direction. Gradual, layer-by-layer current reduction improves the bottom molding and performance, and the deposition efficiency, and stabilizes the process. Scanning speed enhancement or cooling time reduction destabilizes the end formation, reduces the effective deposition rate, and slightly degrades the performance. All deposited samples are distinctly anisotropic, but satisfy the industrial standard. Overall, deposition in speed cold welding mode, with 10 s cooling time, 30 cm/min scanning speed, and gradually reduced bottom current exhibits good stability, and the molding efficiency and mechanical properties are optimal.