End-to-end Speech Translation is hindered by a lack of available data resources. While most of them are based on documents, a sentence-level version is available, which is however single and static, potentially impeding the usefulness of the data. We propose a new data augmentation strategy, SegAugment, to address this issue by generating multiple alternative sentence-level versions of a dataset. Our method utilizes an Audio Segmentation system, which re-segments the speech of each document with different length constraints, after which we obtain the target text via alignment methods. Experiments demonstrate consistent gains across eight language pairs in MuST-C, with an average increase of 2.5 BLEU points, and up to 5 BLEU for low-resource scenarios in mTEDx. Furthermore, when combined with a strong system, SegAugment establishes new state-of-the-art results in MuST-C. Finally, we show that the proposed method can also successfully augment sentence-level datasets, and that it enables Speech Translation models to close the gap between the manual and automatic segmentation at inference time.