Automating the peeling of soft, easily deformable fruits such as mandarin oranges remains a significant challenge in robotics, as traditional blade-based cutting methods often cause damage to the flesh. To overcome this limitation, this paper proposes a novel robotic peeling system utilizing an “interfacial insertion” approach inspired by human finger movements. We developed a custom fingernail-equipped end effector and a 3D trajectory generation algorithm based on point cloud data. The system calculates surface tangents and normal vectors to apply a specific depth offset, safely guiding the nail between the peel and the flesh. Furthermore, a multi-view point cloud integration method was introduced to overcome camera blind spots. Experimental results using a dual-arm robot demonstrated the feasibility of continuous peeling from the top to the bottom of the fruit.