Segmenting breast mass from magnetic resonance imaging (MRI) scans is an important step in the breast cancer diagnostic procedure for physicians and computer-aided diagnosis systems. Sufficient high-quality annotation is essential for establishing an automatic segmentation model, particularly for MRI breast masses with complex backgrounds and various sizes. In this study, we have proposed a novel approach for training an MRI breast mass segmentation network with partial annotations and reinforcing it with two weakly supervised constraint losses. Specifically, following three user-friendly partial annotation methods were designed to alleviate annotation costs: single-slice, orthogonal slice, and interval slice annotations. With the guidance of partial annotations, we first introduced a volume awareness loss that supports the additional constraint for masses with various scales. Moreover, to reduce false-positive predictions, we proposed an end-to-end differentiable outlier-suppression loss to suppress noise activation outside the target during training. We validated our method on 140 patients. The Dice similarity coefficient (DSC) of the proposed three partial annotation methods are 0.674, 0.835, and 0.837 respectively. Quantitative and qualitative evaluations demonstrate that our method can achieve competitive performance compared to state-of-the-art methods with complete annotations. (c) 2022 Published by Elsevier B.V.