The segmentation of quasi-periodic time series (QTS) is crucial for modeling analysis in industrial and medical fields. However, it is challenging to automatically and effectively split different types of QTSs under the same settings. To address this issue, we propose an enhanced graph-based QTS automatic segmentation (EGQAS) framework that integrates an enhanced graph structure and hybrid clustering. The enhanced graph structure improves the stability of QTS segmentation, especially for a large number of QTS, by using edge weight filtering and aggregation. Hybrid clustering, which consists of hierarchical clustering and a modified k-means algorithm, removes clusters with outliers and incomplete divisions to improve the integrity of the final QTS split points. For four different types of public datasets, EGQAS outperforms the current state-of-the-art baselines, demonstrating its better adaptability. In tests with the MIT-BIH arrhythmia database (MITDB), EGQAS proves itself to be effective and stable with a large number of data.