Current disfluency detection models focus on individual utterances each from a single speaker. However, numerous discontinuity phenomena in spoken conversational transcripts occur across multiple turns, which can not be identified by disfluency detection models. This study addresses these phenomena by proposing an innovative Multi-Turn Cleanup task for spoken conversational transcripts and collecting a new dataset, MultiTurnCleanup. We design a data labeling schema to collect the high-quality dataset and provide extensive data analysis. Furthermore, we leverage two modeling approaches for experimental evaluation as benchmarks for future research.