Accurate segmentation of the optic cup and optic disc is crucial for glaucoma diagnosis through the vertical cup-to-disc ratio. Prevailing fully-supervised deep learning methods, however, rely on pixel-level annotations, which are labor intensive and costly to obtain. While weakly supervised approaches leveraging foundational models like SAM with bounding box prompts reduce this dependency, they often yield suboptimal performance on fundus images due to the inherently ambiguous boundaries of ocular structures. This work addresses the challenging task of generating high-quality segmentation masks from sparse bounding-box annotations. We propose SCAM-Net, a novel instance segmentation framework designed for a practical mixed-supervision setting, which synergistically utilizes both limited pixel-level ground truth and abundant, cost-effective box annotations for accurate optic cup and optic disc segmentation. Our framework introduces a high-performance pseudo-label generation strategy that fuses the semantic localization from Class Activation Maps with the fine-grained details from the Segment Anything Model, effectively translating sparse annotations into dense, high-fidelity pixel-level guidance. Furthermore, we introduce a pixel-level contrastive learning mechanism that leverages these generated pseudo masks as priors. By explicitly contrasting features between foreground and background regions, our method enhances feature discriminability, significantly improving segmentation accuracy at the challenging, low-contrast optical cup and optic disc boundaries. Extensive experiments on three public datasets, Drishti-GS, RIM-ONE, and REFUGE, demonstrate that SCAM-Net substantially outperforms existing state-of-the-art methods. By achieving precise segmentation with easily accessible bounding box annotations, our work presents a cost-effective and highly efficient solution for automated glaucoma screening.