The current paradigm of robot-assisted surgeries (RASs) depends entirely on an individual surgeon's manual capability. Autonomous robotic surgery - removing the surgeon's hands - promises enhanced efficacy, safety, and improved access to optimized surgical techniques. Surgeries involving soft tissue have not been performed autonomously because of technological limitations, including lack of vision systems that can distinguish and track the target tissues in dynamic surgical environments and lack of intelligent algorithms that can execute complex surgical tasks. We demonstrate in vivo supervised autonomous soft tissue surgery in an open surgical setting, enabled by a plenoptic three-dimensional and near-infrared fluorescent (NIRF) imaging system and an autonomous suturing algorithm. Inspired by the best human surgical practices, a computer program generates a plan to complete complex surgical tasks on deformable soft tissue, such as suturing and intestinal anastomosis. We compared metrics of anastomosis - including the consistency of suturing informed by the average suture spacing, the pressure at which the anastomosis leaked, the number of mistakes that required removing the needle from the tissue, completion time, and lumen reduction in intestinal anastomoses - between our supervised autonomous system, manual laparoscopic surgery, and clinically used RAS approaches. Despite dynamic scene changes and tissue movement during surgery, we demonstrate that the outcome of supervised autonomous procedures is superior to surgery performed by expert surgeons and RAS techniques in ex vivo porcine tissues and in living pigs. These results demonstrate the potential for autonomous robots to improve the efficacy, consistency, functional outcome, and accessibility of surgical techniques.