The purposes are to meet the individual needs of leather production, improve the efficiency of leather cutting, and increase the product’s competitiveness. According to the existing problems in current leather cutting systems, a Fault Diagnosis (FD) method combining Convolutional Neural Network (CNN) and the Support Vector Machine (SVM) of Gray Wolf Optimizer (GWO) is proposed. This method first converts the original signal into a scale spectrogram and then selects the pre-trained CNN model, AlexNet, to extract the signal scale spectrogram’s features. Next, the Principal Component Analysis (PCA) reduces the obtained feature’s dimensionality. Finally, the normalized data are input into GWO’s SVM classifier to diagnose the bearing’s faults. Results demonstrate that the proposed model has higher cutting accuracy than the latest fault detection models. After model optimization, when c is 25 and g is 0.2, the model accuracy can reach 99.24%, an increase of 66.96% compared with traditional fault detection models. The research results can provide ideas and practical references for improving leather cutting enterprises’ process flow.