Currently, diagnostic methods for compound fault of mixed eccentricity and demagnetization (CFMED) in external rotor permanent magnet motors (ERPMMs) still face the challenges of overlapping fault features and scarce training data. Therefore, a new data-driven diagnosis method is proposed for CFMED in ERPMMs in this article. First, an analytical model (AM) of back electromotive force (EMF) of ERPMMs with CFMED is proposed. Then, the bispectrum of back EMF with CFMED is analyzed. Furthermore, based on the proposed AM, large-sample CFMED datasets is efficiently established. Based on the convolutional neural network, a two-step diagnosis model of CFMED is established. Finally, experimental prototypes for simulating CFMED are made, the validity and robustness of the proposed diagnosis model are verified. The proposed method provides a new idea for the diagnosis of CFMED.