This paper details the design, analysis, fabrication, and validation of a deployable, atraumatic grasper intended for retraction and manipulation tasks in manual and robotic minimally invasive surgical (MIS) procedures. Fabricated using a combination of shape deposition manufacturing (SDM) and 3D printing, the device (which acts as a deployable end-effector for robotic platforms) has the potential to reduce the risk of intraoperative hemorrhage by providing a soft, compliant interface between delicate tissue structures and the metal laparoscopic forceps and graspers that are currently used to manipulate and retract these structures on an ad hoc basis. This paper introduces a general analytical framework for designing SDM fingers where the desire is to predict the shape and the transmission ratio, and this framework was used to design a multijointed grasper that relies on geometric trapping to manipulate tissue, rather than friction or pinching, to provide a safe, stable, adaptive, and conformable means for manipulation. Passive structural compliance, coupled with active grip force monitoring enabled by embedded pressure sensors, helps to reduce the cognitive load on the surgeon. Initial manipulation tasks in a simulated environment have demonstrated that the device can be deployed though a 15 mm trocar and develop a stable grasp using Intuitive Surgical's daVinci robotic platform to deftly manipulate a tissue analog.