Diffusion-based singing voice conversion (SVC) models have shown better synthesis quality compared to traditional methods. However, in cross-domain SVC scenarios, where there is a significant disparity in pitch between the source and target voice domains, the models tend to generate audios with hoarseness, posing challenges in achieving high-quality vocal outputs. Therefore, in this paper, we propose a Self-supervised Pitch Augmentation method for Singing Voice Conversion (SPA-SVC), which can enhance the voice quality in SVC tasks without requiring additional data or increasing model parameters. We innovatively introduce a cycle pitch shifting training strategy and Structural Similarity Index (SSIM) loss into our SVC model, effectively enhancing its performance. Experimental results on the public singing datasets M4Singer indicate that our proposed method significantly improves model performance in both general SVC scenarios and particularly in cross-domain SVC scenarios.