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Segmentation allows localization and visualization of breast lesions of interest, thus essential for precise diagnosis, prognosis and treatment. However, accurate segmentation from magnetic resonance imaging (MRI) faces following challenges: 1) multiscale breast tumors with a large size range; 2) image quality degradation caused by motion artifacts; 3) blurred tumor boundaries especially malignant tumors; 4) limited labeled MR images. To address these challenges, we propose a semi-supervised boundary-guided segmentation network (Semi-BGSegNet) for breast tumors. Specifically, we first construct a boundary-guided baseline segmentation network (BGSegNet) that integrated multi-scale and attention modules to the encoder-decoder architecture. A dynamic boundary loss is combined with the cross-entropy loss to guide the update of BGSegNet. Then, we develop a lightweight pixel-level discriminator to discriminate predictions from labels. The discriminator can also provide pseudo labels for unlabeled data for semi-supervised training of BGSegNet. Experiments demonstrated the effectiveness of our model compared to other supervised and semi-supervised methods.