Slip detection helps prevent robotic hands from dropping grasped objects and would thus enable complex object manipulation. Here we present a method of detecting slip with a biomimetic optical tactile sensor—the TacTip—that operates by measuring the positions of internal pins embedded in its compliant skin. We investigate whether local pin movement is a strong signal of slip. Accurate and robust discrimination between static and slipping objects is obtained with a support vector machine (accuracy 99.88%). We then demonstrate performance on a task in which a slipping object must be caught. For fast reaction times, a modified TacTip is made for high-speed data collection. Performance of the slip detection method is then validated under several test conditions, including varying the speed at which slip onset occurs and using novel shaped objects. The proposed methods should apply to tactile sensors that can detect the local velocities of surface movement. The sensor and slip detection methods are also well-suited for integration onto robotic hands for deploying slip control under manipulation.