Lung cancer has the highest mortality rate among all malignancies. Non-micro pulmonary nodules are the primary manifestation of early-stage lung cancer. If patients can be detected with nodules in the early stage and receive timely treatment, their survival rate can be improved. Due to the large number of patients and limited medical resources, doctors take a longer time to make a diagnosis, which reduces efficiency and accuracy. Besides, there are no suitable approaches for developing countries. Therefore, we propose a 2.5D-based cascaded multi-stage framework for automatic detection and segmentation (DS-CMSF) of pulmonary nodules. The first three stages of the framework are used to discover lesions, and the latter stage is used to segment them. The first locating stage introduces the classical 2D-based Yolov5 model to locate the nodules roughly on axial slices. The second aggregation stage proposes a candidate nodule selection (CNS) algorithm to locate further and reduce redundant candidate nodules. The third classification stage uses a multi-size 3D-based fusion model to accommodate nodules of varying sizes and shapes for false-positive reducing. The last segmentation stage introduces multi-scale and attention modules into 3D-based UNet autoencoder to segment the nodular regions finely. Our proposed framework achieves 95.95% sensitivity and 89.50% CPM for nodules detection on the LUNA16 dataset, and 86.75% DSC for nodules segmentation on the LIDC-IDRI dataset. Moreover, our approach also achieves the accuracy-complexity trade-off, which can effectively realize the auxiliary diagnosis of pulmonary nodules in developing countries.