Discrete representation has shown advantages in speech generation tasks, wherein discrete tokens are derived by discretizing hidden features from self-supervised learning (SSL) pre-trained models. However, the direct application of speech SSL models to singing generation encounters domain gaps between speech and singing. Furthermore, singing generation necessitates a more refined representation than typical speech. To address these challenges, we introduce SingOMD, a novel method to extract singing-oriented multi-resolution discrete representations from speech SSL models. Specifically, we first adapt the features from speech SSL through a resynthesis task and incorporate multi-resolution modules based on resampling to better serve singing generation. These adapted multi-resolution features are then discretized via clustering. Extensive experiments demonstrate the robustness, efficiency, and effectiveness of these representations in singing vocoders and singing voice synthesis.