The earlier diagnosis of brain tumors is a critical challenge that influences treatment and facilitates prompt detection of the disease. Conventional MRI provides a structural and functional view of the tumors. On the other hand, recent deep learning-based algorithms, particularly single-stage convolutional neural network-based models, face challenges in providing the exact location of the tumor as well as in enhancing detection and classification accuracy. This is due to a lack of global-local integration of features, lack of spatial consistency, and low resistance to intensity variation, which are typical of clinical MRI scans. In order to address these gaps, the proposed research uses the DSC-SwinNet algorithm, which consists of a dual-stage transformer structure primarily utilized for tumor segmentation and classification. The first step employs a Swin Transformer-based encoder-decoder that uses window-based multi-head self-attention to simultaneously obtain local lesion features and long-range global contextual features of multi-modal MRI volumes. The next stage, known as Dual-stage Classification (DSC), is responsible for incorporating the ROI characteristics with conceptual representations of the tumor to identify the type of tumor. The proposed DSC-SwinNet has a Dice score of 0.934, an IoU of 0.891, an HD95 of 3.70 mm, achieving a classification accuracy of 97.8%, an F1-score of 97.9%, and an AUC of 0.99 on the BraTS multi-modal MRI data, demonstrating the potential of DSC-SwinNet as a clinically reliable brain tumor analyzer.