The tactile sensing capabilities of human hands are essential in performing daily activities. Simultaneously perceiving normal and shear forces via the mechanoreceptors integrated into the hands enables humans to achieve daily tasks like grasping delicate objects. In this paper, we design and fabricate a novel biomimetic tactile sensor with skin-like heterogeneity that perceives normal and shear contact forces simultaneously. It mimics the multilayers of mechanoreceptors by combining an extrinsic layer (piezoresistive sensors) and an intrinsic layer (a Hall sensor) so that it can perform estimation of contact force directions, locations, and joint-level torque. By integrating our sensors, a robotic gripper can obtain contact force feedback at fingertips; accordingly, robots can perform challenging tasks, such as tweezers usage, and egg grasping. This insightful sensor design can be customized and applied in different areas of robots and provide them with heterogeneous force sensing, potentially supporting robotics in acquiring skin-like tactile feedback.