This study focuses on developing a fiber-reinforced woven composite material with auxetic properties, characterized by a negative Poisson’s ratio. Auxetic materials have been shown to exhibit superior mechanical performance compared to conventional materials, offering enhanced resistance to compression, impact, and fracture. While much research has focused on architected auxetic materials, fiber-reinforced auxetic composites have received less attention. The intended application of these materials is in automotive decoupling mounts, where their dynamic and mechanical performance is evaluated. The composite material in this study is created using a 3D hollow multilayer fabric formed from a bi-component yarn, consisting of a thermoplastic core (acting as resin) and aramid multifilament (acting as reinforcement). The fabric is thermoformed to create an auxetic honeycomb structure with re-entrant hexagons. Although this geometry has been widely studied through various analytical methods, the effects of woven reinforcement-induced anisotropy on the material’s behavior need to be experimentally investigated. The paper presents the compressive mechanical response of the multicellular auxetic composite, with a focus on the deformation ratio of the overall structures.