Detecting and segmenting dysfluencies is crucial for effective speech therapy and real-time feedback. However, most methods only classify dysfluencies at the utterance level. We introduce StutterCut, a semi-supervised framework that formulates dysfluency segmentation as a graph partitioning problem, where speech embeddings from overlapping windows are represented as graph nodes. We refine the connections between nodes using a pseudo-oracle classifier trained on weak (utterance-level) labels, with its influence controlled by an uncertainty measure from Monte Carlo dropout. Additionally, we extend the weakly labelled FluencyBank dataset by incorporating frame-level dysfluency boundaries for four dysfluency types. This provides a more realistic benchmark compared to synthetic datasets. Experiments on real and synthetic datasets show that StutterCut outperforms existing methods, achieving higher F1 scores and more precise stuttering onset detection.