Biomedical segmentation networks easily suffer from the unexpected misclassification between foreground and background objects when learning on limited and imperfect medical datasets. Inspired by the strong power of Out-of-Distribution (OoD) data on other visual tasks, we propose a data-centric framework, Med-OoD to address this issue by introducing OoD data supervision into fully-supervised biomedical segmentation with none of the following needs: (i) external data sources, (ii) feature regularization objectives, (iii) additional annotations. Our method can be seamlessly integrated into segmentation networks without any modification on the architectures. Extensive experiments show that Med-OoD largely prevents various segmentation networks from the pixel misclassification on medical images and achieves considerable performance improvements on Lizard dataset. We also present an emerging learning paradigm of training a medical segmentation network completely using OoD data devoid of foreground class labels, surprisingly turning out 76.1% mIoU as test result. We hope this learning paradigm will attract people to rethink the roles of OoD data. Code is made available at https://github.com/StudioYG/Med-OoD.