Wire and arc additive manufacturing (WAAM) employing a magnesium (Mg) alloy is superior in terms of safety, energy efficiency, and deposition rate when compared with a process that utilizes lasers and powder materials. However, problems with WAAM employing an Mg alloy include poor dimensional accuracy due to low viscosity of the molten Mg alloy. In addition, since Mg alloys cause a combustion reaction with water, an effective cooling method, such as direct water cooling, cannot be applied. In this study, a solid contact-based active cooling method employing copper blocks with high thermal conductivity was proposed to improve the dimensional accuracy and cooling efficiency of fabricated objects using AZ31. Moreover, the proposed method renders it possible to fabricate a wall structure with high flatness as the molten AZ31 solidifies upon direct contact with the flat surface of copper blocks. In addition, the copper blocks harboring an internal water circulation system achieved a higher cooling efficiency and shortened the interval cooling time between the deposition of subsequent layers. Meanwhile, it was discovered that the arc deflected toward the copper blocks, not onto the substrate or the previous layer when the wire tip approached too close to the blocks.