Double arrowhead honeycombs (DAHs) are a type of auxetic materials, i.e., showing negative Poisson's ratio (NPR), and are promising for energy absorption applications. Their in-plane impact responses are theoretically and numerically explored. Theoretical models for the collapse stress under quasi-static, low-velocity, and high-velocity impacts are developed, based upon the corresponding microstructural deformation modes. Obtained results show that the collapse stress under quasi-static and low velocity impacts depends upon the two re-entrant angles responsible for NPR, while it is insensitive to them under high-velocity impact. The developed theoretical models are employed to analyze the energy absorption capacity of DAHs, showing the absorbed energy under high-velocity impact approximately proportional to the second power of velocity. Extension of the high-velocity impact model to functionally graded (FG) DAHs is also discussed. Good agreement between the theoretical and finite element (FE) predictions on the impact responses of DAHs is obtained.