Cochlear implant surgery is a treatment for individuals with severe hearing loss. It involves inserting an array of electrodes inside the cochlea to electrically stimulate the auditory nerve and restore hearing sensation. A crucial step in this procedure is mastoidectomy, a surgical intervention that removes part of the mastoid region of the temporal bone, providing a critical pathway to the cochlea for electrode placement. Accurate prediction of the mastoidectomy region from preoperative imaging assists presurgical planning, reduces surgical risks, and improves surgical outcomes. In previous work, a self-supervised network was introduced to predict the mastoidectomy region using only preoperative CT scans. While promising, the method suffered from suboptimal robustness, limiting its practical application. To address this limitation, we propose a novel weakly-supervised Mamba-based framework to predict accurate mastoidectomy regions directly from preoperative CT scans. Our approach utilizes a 3D T-Distribution loss function inspired by the Student-t distribution, which effectively handles the complex geometric variability inherent in mastoidectomy shapes. Weak supervision is achieved using the segmentation results from the prior self-supervised network to eliminate the need for manual data cleaning or labeling throughout the training process. The proposed method is extensively evaluated against state-of-the-art approaches, demonstrating superior performance in predicting accurate and clinically relevant mastoidectomy regions. Our findings highlight the robustness and efficiency of the weakly-supervised learning framework with the proposed novel 3D T-Distribution loss.