This study emphasizes the criticality of measuring specific cutting energy in machining Hastelloy C276 for biomedical industry applications, offering valuable insights into machinability and facilitating the optimization of tool selection, cutting parameters, and process efficiency. The research employs artificial intelligence-assisted meta-models for cost-effective and accurate predictions of specific cutting energy consumption. Comparative analyses conducted on Hastelloy C276, utilizing a TiAlN-coated solid carbide insert across various media (dry, MQL, LN2, and MQL+LN2), reveal the superiority of hybrid LN2+MQL in reducing specific cutting energy consumption. Subsequently, the analysis of variance underscores the cutting speed as the most influential parameter as compared to other inputs. Finally, a statistical evaluation compares the Gene Expression Programming (GEP) model against the Artificial Neural Network (ANN), and Response Surface Methodology model, demonstrating the superior predictive performance of the GEP meta-model. The GEP model demonstrates validation results with an error range of 0.25%–1.52%, outperforming the ANN and RSM models, which exhibit an error range of 0.49%–8.33% and 2.68%–10.18%, respectively. This study suggests the potential integration of contemporary intelligent methodologies for sustainable superalloy machining in biomedical industry applications, providing a foundation for enhanced productivity and reduced environmental impact of surgical instrument and biomedical device machining.