Tunnel lining crack is a crucial indicator of tunnels' safety status. Aiming to classify and segment tunnel cracks with enhanced accuracy and efficiency, this study proposes a two-step deep learning-based method. An automatic tunnel image classification model is developed using the DenseNet-169 in the first step. The proposed crack segmentation model in the second step is based on the DeepLabV3+, whose internal logic is evaluated via a score-weighted visual explanation technique. Proposed method combines tunnel image classification and segmentation together, so that the selected images containing cracks from the first step are segmented in the second step to improve the detection accuracy and efficiency. The superior performances of the two-step method are validated by experiments. The results show that the accuracy and frames per second (FPS) of the tunnel crack classification model are 92.23% and 39.80, respectively, which are higher than other convolutional neural networks (CNN) based and Transformer based models. Also, the intersection over union (IoU) and F1 score of the tunnel crack segmentation model are 57.01% and 67.44%, respectively, outperforming other state-of-the-art models. Moreover, the provided visual explanations in this study are conducive to understanding the "black box" of deep learning-based models. The developed two-stage deep learning-based method integrating visual explanations provides a basis for fast and accurate quantitative assessment of tunnel health status.