Based on the problem of incomplete mining of Additive Manufacturing (AM) potential caused by the limitations of current Design for Additive Manufacturing (DFAM) methods, this paper proposes to integrate Additive Manufacturing and axiomatic design to obtain the global conceptual design method of products to be manufactured with AM. In response to the lower process dependence of AM technology compared to traditional processes, two integration measures of “influence region division” and “process domain forward” are proposed, and finally, the axiomatic design process for AM is obtained. Taking the assembly-free integrated design of mechanical fingers imitating dexterous hands as an example, the conceptual design method studied was validated. The application of innovative features such as flexible finger joints and lattice-filled finger joints shows that the design method proposed in this paper can deeply tap into the manufacturing potential of AM, achieve lightweight and integrated molding of products, which provides useful references for designers.