Accurately segmenting cancer lesions is essential for effective personalized treatment and enhanced patient outcomes. We propose a multi-resolution selective segmentation (MurSS) model to accurately segment breast cancer lesions from hematoxylin and eosin (H&E) stained whole-slide images (WSIs). We used The Cancer Genome Atlas breast invasive carcinoma (BRCA) public dataset for training and validation. We used the Korea University Medical Center, Guro Hospital, BRCA dataset for the final test evaluation. MurSS utilizes both low- and high-resolution patches to leverage multi-resolution features using adaptive instance normalization. This enhances segmentation performance while employing a selective segmentation method to automatically reject ambiguous tissue regions, ensuring stable training. MurSS rejects 5% of WSI regions and achieves a pixel-level accuracy of 96.88% (95% confidence interval (CI): 95.97-97.62%) and mean Intersection over Union of 0.7283 (95% CI: 0.6865-0.7640). In our study, MurSS exhibits superior performance over other deep learning models, showcasing its ability to reject ambiguous areas identified by expert annotations while using multi-resolution inputs.