Quad-plane is a popular type of electric vertical and takeoff/landing (eVTOL) vehicle that hybridizes a quadrotor and a fixed-wing airplane. However, the mechanical simplicity of a quad-plane also makes it vulnerable to rotor failures. When a complete rotor fails, it becomes physically impossible to stop the quad-plane from fast yaw spinning, which further induces considerable abnormal aerodynamic forces and moments on the wing. In this paper, a novel incremental adaptive sliding mode control (I-ASMC) is proposed to address these challenges. First, by exploiting sensor measurements, it simultaneously reduces the control model dependency and the minimum possible sliding mode control/observer gains. Second, finite-time convergence is guaranteed in the Lyapunov sense. Third, the control gains are automatically adapted to their minimum possible values without prior-knowledge on the uncertainty bounds. The proposed I-ASMC method is verified on a high fidelity simulation platform with computational fluid dynamic (CFD) aerodynamic models. Simulation results demonstrate that I-ASMC can drive a quad-plane with a complete loss of a single rotor to follow a trajectory. Its robustness to aerodynamic model uncertainties and rotor faults is also better than the linear quadratic regulator (LQR) and the incremental nonlinear dynamic inversion (INDI) control. In conclusion, the reduced model dependency, implementation simplicity, and improved robustness make the proposed I-ASMC promising for enhancing quad-plane safety in real life.