We introduce GroupSketch, a novel method for vector sketch animation that effectively handles multi-object interactions and complex motions. Existing approaches struggle with these scenarios, either being limited to single-object cases or suffering from temporal inconsistency and poor generalization. To address these limitations, our method adopts a two-stage pipeline comprising Motion Initialization and Motion Refinement. In the first stage, the input sketch is interactively divided into semantic groups and key frames are defined, enabling the generation of a coarse animation via interpolation. In the second stage, we propose a Group-based Displacement Network (GDN), which refines the coarse animation by predicting group-specific displacement fields, leveraging priors from a text-to-video model. GDN further incorporates specialized modules, such as Context-conditioned Feature Enhancement (CCFE), to improve temporal consistency. Extensive experiments demonstrate that our approach significantly outperforms existing methods in generating high-quality, temporally consistent animations for complex, multi-object sketches, thus expanding the practical applications of sketch animation.