Functionally graded materials (FGM) have attracted considerable interest in advanced engineering applications due to their ability to show spatially tailored properties in three dimensions. This characteristic enables the controlled adjustment of mechanical, thermal, and dynamic responses to meet specific performance requirements. In this context, auxetic composites are notable for their enhanced energy absorption capacity, improved shear resistance, and increased fracture toughness [1, 2]. This work investigates the static bending and free-vibration behavior of through-thickness FGM beams incorporating auxetic architectures and carbon nanotube (CNT) reinforcement. The material system consists of a continuous exponential gradation between a metallic matrix and a ceramic phase, with optional reinforcement by uniformly dispersed single-walled carbon nanotubes. In the beam plane, a periodic reentrant hexagonal honeycomb geometry is employed to induce auxetic behavior. The analyses are conducted using first-order shear deformation theory, incorporating case-specific shear correction factors that account for the combined effects of material gradation and cellular geometry. A finite element formulation is used to evaluate transverse deflections, natural frequencies, and shear correction factors across a broad parameter space, including auxetic cell angle, geometric aspect ratios, ceramic phase type, and CNT weight fraction. The results show that auxetic geometry plays a dominant role in shear and dynamic responses, with pronounced sensitivity observed for moderate re-entrant angles, while non-auxetic configurations exhibit parameter-independent behavior. CNT reinforcement generally increases stiffness and modifies shear correction factors, though its effect depends on both geometry and material composition. To support the interpretation of the large parametric dataset, an unsupervised machine learning approach based on K-means clustering is applied. The clustering analysis identifies response-based groupings associated with distinct mechanical behaviors, providing additional insight into design-relevant trends and supporting informed selection of viable configurations.