Detecting singing voice deepfakes, or SingFake, involves determining the authenticity and copyright of a singing voice. Existing models for speech deepfake detection have struggled to adapt to unseen attacks in this unique singing voice domain of human vocalization. To bridge the gap, we present a groundbreaking SingGraph model. The model synergizes the capabilities of the MERT acoustic music understanding model for pitch and rhythm analysis with the wav2vec2.0 model for linguistic analysis of lyrics. Additionally, we advocate for using RawBoost and beat matching techniques grounded in music domain knowledge for singing voice augmentation, thereby enhancing SingFake detection performance. Our proposed method achieves new state-of-the-art (SOTA) results within the SingFake dataset, surpassing the previous SOTA model across three distinct scenarios: it improves EER relatively for seen singers by 13.2%, for unseen singers by 24.3%, and unseen singers using different codecs by 37.1%.