Anti-chiral metastructures made up of ring nodes and elastic bending ligaments provide excellent flexibility in design for compliant architecture. Metastructures with auxetic behavior are known for their enhanced energy absorption. In this article, the Poisson’s ratio and damping properties of the anti-trichiral architecture and sandwich composite are studied. The nucleus and the sandwiches are made from the same bio-based material which is polylactic acid PLA reinforced with flax fibers. Additive manufacturing technology is used to fabricate the specimens. Uniaxial tensile tests are performed on the anti-trichiral nuclei. Vibration tests were conducted on the auxetic nuclei, face sheets and sandwich structures with a clamp-free configuration. Those tests are carried out on specimens with different geometric parameters of the anti-trichiral unit cell in order to study their effect on the static and dynamic properties of this metastructure. In addition, a finite element model was used to estimate the Poisson’s ratio values. The experimental and numerical results were in close agreement. The results show that the structural Poisson’s ratio of the anti-trichiral nucleus largely depends on the radius (r) of the cylindrical nodes of the unit cell. The results also show that the damping properties of the auxetic structure depend on the radius (r).