Cellular metamaterials can be designed to have increased energy absorption capacity and higher specific stiffness while retaining light weightiness. In this research, a unique cellular metamaterial with an axisymmetric chiral auxetic structure was designed, fabricated, and mechanically tested. The 3D chiral unit cell corresponds to the 10th eigenmode of the regular cubic unit cell. The 3D chiral unit cells were spatially scaled and distributed in the radial and axial directions to form the axisymmetric chiral auxetic structure. The unit cells were graded in the radial direction by scaling the length and amplitude of the horizontal struts from the inner to the outer layer of cells. The designed structure was fabricated using the powder fusion method (PBF) with basic material 316L and then experimentally tested in quasi-static and dynamic compression loading regimes, achieving strain rates from 0.005 s-1 to 1050 s-1. The tested structure exhibited pronounced auxetic response with smooth deformation and gradually increasing load-carrying capability until final densification. Digital cameras observed the structures' deformation process, and the advanced Digital Image Correlation (DIC) method was used to analyse the full-field strain data. The computational model of the novel chiral auxetic structure was built and validated by the experimental results. The validated computational model was then used to optimise the axisymmetric chiral auxetic structure parameters to achieve the desired mechanical response.