A novel auxetic structure applicable to airless tire spokes is designed based on the primitive-type triply periodic minimal surface (P-TPMS) to have higher stiffness through deformation under compressive force. For becoming higher stiffness by deformation, an unit cell of auxetic structure is proposed and its characteristics according to design parameters are studied. Based on the parametric study, a rotated primitive-type auxetic structure (RPAS) is designed, and the deformative behaviors of an airless tire with the RPAS spokes are compared with a generally used honeycomb spoke. Simulation and experiment results show that the designed RPAS tire exhibits more stable behavior through higher rigidity depending on the deformation state when compressed on flat ground and obstacles. This variable stiffness characteristic of RPAS tires can be advantageous for shock absorption and prevention of large local deformations. Also, the manufacturability of the designed auxetic structure is evaluated using real rubber-based additive manufacturing processes for practical application in the tire manufacturing industry.