Traditional sequential recommendation methods assume that users' sequence data is clean enough to learn accurate sequence representations to reflect user preferences. In practice, users' sequences inevitably contain noise (e.g., accidental interactions), leading to incorrect reflections of user preferences. Consequently, some pioneer studies have explored modeling sequentiality and correlations in sequences to implicitly or explicitly reduce noise's influence. However, relying on only available intra-sequence information (i.e., sequentiality and correlations in a sequence) is insufficient and may result in over-denoising and under-denoising problems (OUPs), especially for short sequences. To improve reliability, we propose to augment sequences by inserting items before denoising. However, due to the data sparsity issue and computational costs, it is challenging to select proper items from the entire item universe to insert into proper positions in a target sequence. Motivated by the above observation, we propose a novel framework--Self-augmented Sequence Denoising for sequential Recommendation (SSDRec) with a three-stage learning paradigm to solve the above challenges. In the first stage, we empower SSDRec by a global relation encoder to learn multi-faceted inter-sequence relations in a data-driven manner. These relations serve as prior knowledge to guide subsequent stages. In the second stage, we devise a self-augmentation module to augment sequences to alleviate OUPs. Finally, we employ a hierarchical denoising module in the third stage to reduce the risk of false augmentations and pinpoint all noise in raw sequences. Extensive experiments on five real-world datasets demonstrate the superiority of \model over state-of-the-art denoising methods and its flexible applications to mainstream sequential recommendation models. The source code is available at https://github.com/zc-97/SSDRec.