Robots equipped with bionic skins for enhancing the robot perception capability are increasingly deployed in wide applications ranging from healthcare to industry. Artificial intelligence algorithms that can provide bionic skins with efficient signal processing functions further accelerate the development of this trend. Inspired by the somatosensory processing hierarchy of humans, the bioinspired co-design of a tactile sensor and a deep learning-based algorithm is proposed herein, simplifying the sensor structure while providing computation-enhanced tactile sensing performance. The soft piezoresistive sensor, based on the carbon black-coated polyurethane sponge, offers a continuous sensing area. By utilizing a customized deep neural network (DNN), it can detect external tactile stimulus spatially continuously. Besides, a novel data augmentation method is developed based on the sensor's hexagonal structure that has a sixfold rotation symmetry. It can significantly enhance the generalization ability of the DNN model by enriching the collected training data with generated pseudo-data. The functionality of the sensor and the robustness of the proposed data augmentation strategy are verified by precisely recognizing five touch modalities, illustrating a well-generalized performance, and providing a promising application prospect in human-robot interaction.