Mulberry leaves feed Bombyx mori silkworms to generate silk thread. Diseases that affect mulberry leaves have reduced crop and silk yields in sericulture, which produces 90% of the world's raw silk. Manual leaf disease identification is tedious and error-prone. Computer vision can categorize leaf diseases early and overcome the challenges of manual identification. No mulberry leaf deep learning (DL) models have been reported. Therefore, in this study, two types of leaf diseases: leaf rust and leaf spot, with disease-free leaves, were collected from two regions of Bangladesh. Sericulture experts annotated the leaf images. The images were pre-processed, and 6,000 synthetic images were generated using typical image augmentation methods from the original 764 training images. Additional 218 and 109 images were employed for testing and validation respectively. In addition, a unique lightweight parallel depth-wise separable CNN model, PDS-CNN was developed by applying depth-wise separable convolutional layers to reduce parameters, layers, and size while boosting classification performance. Finally, the explainable capability of PDS-CNN is obtained through the use of SHapley Additive exPlanations (SHAP) evaluated by a sericulture specialist. The proposed PDS-CNN outperforms well-known deep transfer learning models, achieving an optimistic accuracy of 95.05 ± 2.86% for three-class classifications and 96.06 ± 3.01% for binary classifications with only 0.53 million parameters, 8 layers, and a size of 6.3 megabytes. Furthermore, when compared with other well-known transfer models, the proposed model identified mulberry leaf diseases with higher accuracy, fewer factors, fewer layers, and lower overall size. The visually expressive SHAP explanation images validate the models' findings aligning with the predictions made the sericulture specialist. Based on these findings, it is possible to conclude that the explainable AI (XAI)-based PDS-CNN can provide sericulture specialists with an effective tool for accurately categorizing mulberry leaves.