As one of the critical branches of medical image processing, the task of segmentation of breast cancer tumors is of great importance for planning surgical interventions, radiotherapy and chemotherapy. Breast cancer tumor segmentation faces several challenges, including the inherent complexity and heterogeneity of breast tissue, the presence of various imaging artifacts and noise in medical images, low contrast between the tumor region and healthy tissue, and inconsistent size of the tumor region. Furthermore, the existing segmentation methods may not fully capture the rich spatial and contextual information in small-sized regions in breast images, leading to suboptimal performance. In this paper, we propose a novel breast tumor segmentation method, called the transformer and graph convolutional neural (TS-GCN) network, for medical imaging analysis. Specifically, we designed a feature aggregation network to fuse the features extracted from the transformer, GCN and convolutional neural network (CNN) networks. The CNN extract network is designed for the image's local deep feature, and the transformer and GCN networks can better capture the spatial and context dependencies among pixels in images. By leveraging the strengths of three feature extraction networks, our method achieved superior segmentation performance on the BUSI dataset and dataset B. The TS-GCN showed the best performance on several indexes, with Acc of 0.9373, Dice of 0.9058, IoU of 0.7634, F1 score of 0.9338, and AUC of 0.9692, which outperforms other state-of-the-art methods. The research of this segmentation method provides a promising future for medical image analysis and diagnosis of other diseases.