Auxetic structures, characterized by a negative Poisson’s ratio, expand laterally under axial loading and offer superior energy absorption and deformation capacity, making them promising candidates as core materials in sandwich structures. In this study, sandwich panels with three auxetic core geometries (star-4, re-entrant, and honeycomb) were fabricated using fused filament fabrication (FFF). The cores were produced using three thermoplastic materials: polylactic acid (PLA), polyethylene terephthalate glycol (PETG), and carbon fiber-reinforced polyamide (ePAHT-CF). PLA was also used for the face sheets, printed in three orientations (0°, 0/90°, and ±45°) to evaluate anisotropy effects. Mechanical performance was assessed through three-point bending tests, focusing on peak load, energy absorption (EA), and specific energy absorption (SEA). The honeycomb core with PLA face sheets at 0° yielded the highest peak load (702.97 N), a 351% increase compared to the lowest-performing specimen (star-4/ePAHT-CF at 155.76 N). The highest EA (9.64 J) and SEA (0.52 J/g) were achieved by the honeycomb/ePAHT-CF core with ±45° orientation. ANOVA results confirmed that core geometry and material type significantly affect peak load. Overall, the mechanical behavior is governed by the synergistic effects of geometry, material, and printing parameters.