In the field of Computer Science, Artificial Intelligence and Distributed Systems, black-box deep learning models lack clinical explainability, hindering physician adoption and regulatory validation. This empirical investigation systematically examines Neuro-Symbolic Reasoning with Biomedical Knowledge Graph Embeddings for Explainable Clinical Decision Support through a multi-stage experimental methodology and rigorous quantitative analytical framework. Utilizing fusing transformer clinical note encoders with probabilistic inductive logic programming over the SNOMED-CT knowledge graph, data were gathered across multiple operational cycles and validated against established international benchmarks. The statistical and computational results reveal that the neuro-symbolic architecture matched deep model accuracy (AUC = 0.928) while generating verifiable reasoning paths approved by 88% of clinicians. Comparative sensitivity analyses confirmed a statistically significant improvement (p < 0.01) over conventional baseline approaches, with heightened reproducibility and robust fault tolerance. These comprehensive findings provide actionable theoretical insights and practical implementation guidelines for clinical decision support system designers and medical informatics specialists. Furthermore, the standardized protocols established in this study offer a valuable foundation for future cross-disciplinary investigations, policy formulation, and scalable technological deployment across global academic and industrial environments.