Laser additive manufacturing (LAM) of complex-shaped metallic components offers great potential for fabricating customized endovascular stents. In this study, anti-tetrachiral auxetic stents with negative Poisson ratios (NPR) were designed and fabricated via LAM. Poisson’s ratios of models with different diameters of circular node (DCN) were calculated using finite element analysis (FEA). The experimental method was conducted with the LAM-fabricated anti-tetrachiral stents to validate their NPR effect and the simulation results. The results show that, with the increase in DCN from 0.6 to 1.5 mm, the Poisson ratios of anti-tetrachiral stents varied from −1.03 to −1.12, which is in line with the simulation results. The interrelationship between structural parameters of anti-tetrachiral stents, their mechanical properties and biocompatibility was demonstrated. The anti-tetrachiral stents with a DCN of 0.9 mm showed the highest absolute value of negative Poisson’s ratio, combined with good cytocompatibility. The cytocompatibility tests indicate the envisaged cell viability and adhesion of the vascular endothelial cell on the LAM-fabricated anti-tetrachiral auxetic stents. The manufactured stents exhibit great superiority in the application of endovascular stent implantation due to their high flexibility for easy maneuverability during deployment and enough strength for arterial support.