We previously developed the Bio-Pick, Place, and Perfuse (Bio-P3) instrument to fabricate large perfusable tissue constructs by stacking and aligning scaffold-free living microtissues with integrated lumens. The Bio-P3 required an actuating mechanism to manipulate living microtissues of various sizes and shapes that are fragile, and must remain in an aqueous environment. The optical transparency of the Bio-P3 gripping device was essential to provide unobstructed visuals for accurate alignment of microtissues. We previously engineered a pilot fluid force-driven bio-gripper that can pick-and-place microtissue in planar position without causing cellular damage by pulling culture medium through track-etched membrane-integrated cell culture inserts. In this study, we invented a new flexible bio-gripper design that maximized the bio-gripper utilities. We utilized experimental approaches, multivariate analyzes, and theoretical modeling to elucidate how membrane characteristics (pore size, pore density, membrane thickness, membrane area, and surface chemistry) altered bio-gripper robustness and the flow rate (Q(c)) required for successful gripping. We devised two standardized tests and synthetic parts that mimicked microtissues, to systematically quantify bio-gripper performance. All thirteen syringe pump-driven bio-grippers except one successfully gripped and released synthetic parts with values of Q(c) that coincided with our mathematical simulation of the fluid mechanics of gripping. The bio-gripper could grip synthetic parts of various sizes, shapes and masses, demonstrating the robustness of the actuating mechanism. Multivariate analysis of experimental data indicated that both membrane porosity and thickness modulated Q(c), and in addition, revealed that membrane pore density determined membrane optical transparency. Fabricating large tissue constructs requires repeated stacking of microtissues. We showed that one bio-gripper could pick-and-place living microtissues thirty times with Q(c) corresponding to our simulation. Our bio-gripper was capable of stacking and aligning twenty microtissues. In summary, we successfully engineered a robust controllable fluid-driven bio-gripper to efficiently manipulate living microtissues and micro-objects in an aqueous environment.