Objective: This study proposes and preliminarily validates a novel "Functional-Energetic Topology Model" to uncover neurodynamic mechanisms of Non-Suicidal Self-Injury (NSSI), using Graph Neural Networks (GNNs) to decode brain network patterns from single-channel EEG in real-world settings.Methods: EEG data were collected over ~1 month from three adolescents with NSSI using a smartphone app and a portable Fp1 EEG headband during impulsive and non-impulsive states. A theory-driven GNN with seven functional nodes was built. Performance was evaluated via intra-subject (80/20 split) and leave-one-subject-out cross-validation (LOSOCV). GNNExplainer was used for interpretability.Results: The model achieved high intra-subject accuracy (>85%) and significantly above-chance cross-subject performance (approximately73.7%). Explainability analysis revealed a key finding: during NSSI states, a critical feedback loop regulating somatic sensation exhibits dysfunction and directional reversal. Specifically, the brain loses its ability to self-correct via negative bodily feedback, and the regulatory mechanism enters an "ineffective idling" state.Conclusion: This work demonstrates the feasibility of applying theory-guided GNNs to sparse, single-channel EEG for decoding complex mental states. The identified "feedback loop reversal" offers a novel, dynamic, and computable model of NSSI mechanisms, paving the way for objective biomarkers and next-generation Digital Therapeutics (DTx).