A grand challenge of tissue engineering is the fabrication of large constructs with a high density of living cells. By adapting the principles of pick-and-place machines used in the high-speed assembly of electronics, we have developed an innovative instrument, the Bio-Pick, Place, and Perfuse (Bio-P3), which picks up large complex multicellular building parts, transports them to a build area, and precisely places the parts at desired locations while perfusing the parts. These assembled parts subsequently fuse to form a larger contiguous tissue construct. Multicellular microtissues were formed by seeding cells into nonadhesive micro-molds, wherein cells self-assembled scaffold-free parts in the shape of spheroids, toroids, and honeycombs. After removal from the molds, the parts were gripped, transported (using an x, y, z controller), and released using the Bio-P3 with little to no effect on cell viability or part structure. As many as 16 toroids were stacked over a 170 μm diameter post where they fused over the course of 48 h to form a single tissue. Larger honeycomb parts were also gripped and stacked onto a build head that, like the gripper head, provided fluid suction to hold and perfuse the parts during assembly. Scaffold-free building parts help to address several of the engineering and biological challenges to large tissue biofabrication, and the Bio-P3 described in this article is a novel instrument for the controlled gripping, placing, stacking, and perfusing of living building parts for solid organ fabrication.