As a class of metamaterials, auxetic honeycombs have been widely studied and evaluated for a variety of applications. These structures show good mechanical behavior compared to conventional honeycombs. In this article a comparative study of the damping behavior of a hexagonal and re-entrant structure is proposed. Composite structures are made from flax fiber-reinforced Polylactic acid (PLA). Thanks to its viscoelastic behavior, this bio-based and biodegradable composite has more efficient vibration characteristics compared to that made with synthetic fibers. 3D printing technology was used to produce the specimens (sandwich, core and skin). The sandwich is made up of an architectural core and two thin skins. The damping characteristics and dynamic stiffness of this material were assessed through experimental analysis. Several vibration tests were carried out on the beams with a clamp-free configuration. Comparison of material performance shows that the re-entrant core exhibits excellent overall characteristics of lightness, high rigidity and good damping. However, the damping and equivalent stiffness properties of the sandwich with auxetic and conventional core are almost identical. On the other hand, the sandwich structures show a good stiffness/mass ratio and a good loss factor compared with the skin.