Direct-ink-writing (DIW) is an additive manufacturing technique facilitating layer-by-layer printing through the controlled extrusion of customized viscoelastic ink via a fine nozzle, enabling the creation of 3D objects with minimal labor and tooling requirements. A primary challenge in DIW, particularly for thermoset composites, involves formulating a printable ink with suitable rheological attributes, including apparent viscosity, yield stress, and viscoelastic properties, crucial for achieving high shape fidelity in fabricated structures. To address this, a high-performance material system was employed in this study to develop printable ink comprising precursors such as short carbon fiber (40 wt.%), epoxy (55.25 wt.%), silica (2.75 wt.%), and a rheology modifier (2 wt.%), facilitating the fabrication of 10-layer triangular honeycomb composites with different infill densities. Rheological assessments of the ink, including shear rate sweeps ranging from 0.01 to 30 s−1, indicated pronounced shear-thinning behavior, ensuring extrusion through the nozzle even at lower extrusion pressures. Furthermore, stress sweeps ranging from 0.01 to 80 Pa revealed a rapid transition of the ink from a solid-like state to a shear-thinning fluid. Upon the removal of applied stress outside the nozzle, the material reverted to a viscoelastic solid, demonstrating shape fidelity. The resulting honeycomb structures, fabricated using the ink, exactly mimic the digital 3D model, showcasing high print quality. Quasi-static compression tests demonstrated comparable strength and specific strength, measuring at 19.85 ± 4.45 MPa and 27.06 ± 4.38 GPa/g/cc, respectively, suggesting their suitability for use as cores in sandwich structures.