This paper proposes a novel aerial manipulator with front cutting effector (AMFCE) to address the aerial physical interaction (APhI) problem. First, the system uncertainty and external disturbance during the system movement and contact operation are estimated by modeling the entire robot and contact position. Next, based on the established model, the nonlinear disturbance observer (NDO) is used to estimate and compensate the unknown external disturbance of the system and the uncertainty of the model parameters in real time. Then, the nonsingular terminal synovial membrane control method is used to suppress the part that is difficult to estimate. Finally, a controller which is suitable for the movement and operation of the entire system is designed. The controller’s performance is verified through experiments, and the results show that the design, modeling, and control of the entire system can achieve the APhI.