During dexterous manipulation, it is of the utmost importance to avoid dropping the object. It is believed that humans can promptly discern slip and consequently modify grip forces to prevent complete loss of grasp. This paper analyzes and validates two incipient slip detection methods using force and displacement signals from the PapillArray tactile sensor, detecting slip on some of the sensors’ pillars before gross slip occurs. A major contribution of this paper is the development of a novel algorithm that can detect slip caused by either translational or rotational movement of the object relative to the sensor, where previous algorithms were not designed to work for slip caused by rotation. Slip events were independently verified using external camera tracking and subsequently used to evaluate slip detection algorithms operating solely on the PapillArray force and displacement signals. Several algorithm parameters influencing algorithm performance were explored with the goal of optimizing slip detection accuracy. The new algorithm, which can also detect slip for rotational tests, was successful in recognizing slip occurrences using PapillArray data (precision of 85% and recall of 90%), and in detecting incipient slip before gross slip occurs across a range of velocities of translational and rotational movements. Future work will test the algorithms’ effectiveness in real-world object manipulation. Dataset can be found at: https://drive.google.com/drive/folders/1F5Jja89fawynUznJYmozqSKlxcS0JKYC?usp=sharing