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As an interesting energy-absorbing structure, auxetic reentrant honeycomb has attracted much attention in recent decades. Furthermore, due to the adjustable design in the configuration of the graded auxetic reentrant honeycomb (GARH), its mechanical performances were of greater designability and controllability. In this manuscript, compressive properties of the positive gradient auxetic honeycomb (PGAH) and negative gradient auxetic honeycomb (NGAH) were both investigated under different compression velocities. Meanwhile, the negative Poisson's ratio effects on the deformation behaviours and crushing stresses of the PGAH and NGAH were systematically studied. It was found that a new shrinkage deformation mechanism existed in the NGAH, which was different from the dynamic compressive properties of the PGAH and homogeneous auxetic honeycomb in the existing studies. Besides, the energy dissipation characteristics of both the PGAH and NGAH were also investigated. The results showed that, when under the medium and high compression velocities, the energy dissipation of the NGAH were 12.1 times and 7.41 times of those in the PGAH, respectively. It could be indicated that the NGAH was an ideal energy-absorbing structure. [ABSTRACT FROM AUTHOR]