The high-value redesign of discarded products relies on an accurate assessment of their remaining structure and redesign potential. However, existing visual recognition methods struggle to handle product damage, deformation, and occlusion, and lack quantitative assessment methods for redesign value. To address these issues, this paper proposes an end-to-end deep learning joint model that simultaneously performs shape recognition and redesign potential assessment for discarded products. In the shape recognition branch, a multi-branch feature extraction structure and a deformation-robust attention mechanism are designed to capture features of distorted and missing areas. Additionally, a shape structure preservation loss and an edge contrast loss are introduced to enhance boundary segmentation ability. In the potential assessment branch, a three-element index system comprising structural reusability, material integrity, and shape modification freedom is constructed. The spatial topological relationships among components are encoded using graph neural networks, and a shape–potential joint embedding space is established through cross-modal fusion. Continuous potential scores and discrete levels are output in parallel. The model achieves dual-task joint optimization using gradient coordination and an uncertainty weighting strategy. Experiments on our self-built dataset of 12,847 images of discarded electronic products show that the proposed method achieves 66.2% mIoU and 61.4% mAP in the shape recognition task, which are 3.8 and 4.7 percentage points higher than those of Mask2Former, respectively. The local mIoU on damaged areas is improved by 10.7 percentage points to 57.6%. The Spearman rank correlation coefficient between the predicted potential and expert scoring is 0.812, and the mean absolute error is reduced to 0.106. This method provides a quantifiable intelligent decision-making tool for the re-design of discarded products.