The proliferation of signed networks in contemporary social media platforms necessitates robust privacy-preserving mechanisms. Graph unlearning, which aims to eliminate the influence of specific data points from trained models without full retraining, becomes particularly critical in these scenarios where user interactions are sensitive and dynamic. Existing graph unlearning methodologies are exclusively designed for unsigned networks and fail to account for the unique structural properties of signed graphs. Their naive application to signed networks neglects edge sign information, leading to structural imbalance across subgraphs and consequently degrading both model performance and unlearning efficiency. This paper proposes SGU (Signed Graph Unlearning), a graph unlearning framework specifically for signed networks. SGU incorporates a new graph unlearning partition paradigm and a novel signed network partition algorithm that preserve edge sign information during partitioning and ensure structural balance across partitions. Compared with baselines, SGU achieves state-of-the-art results in both model performance and unlearning efficiency.