In industrial practice, it is tough to guarantee repeatable geometries of corrugated veneers with such accuracy as in metal sheets. However, this imperfection can benefit the production and properties of multi-layered cellular wood panels. So far, it has not been verified that the non-repeatability of the shape of wood-based cellular cores is auxetic and whether this disorder changes the mechanical properties and the amount of energy absorbed by the cellular panels. Therefore, the concept of combining irregular corrugated layers manufactured of veneer is proposed to construct a new type of corrugated core for studying the mechanical and energy absorption characteristics of the stiffened sandwich panels, wherein the cellular core possesses a range of negative Poisson's ratio. New wooden auxetic cosine cellular panels were manufactured, further referred to as cosinecomb ones. The research included experimental compression and bending tests, digital image analysis, and analytical and numerical calculations to determine the Poisson's ratios of the cores, the panels' mechanical properties, and their energy absorption capacity. The properties of cores and cosinecomb panels were meticulously evaluated and compared, and the results show that the experimental wave cores formed from wood veneers are auxetic structures with average negative Poisson's ratios equal -0.043 and -0.027 in XY and YX directions, respectively. The contact force, stiffness, strength, and specific absorbed energy of manufactured panels are the highest for the longitudinal orientation of the core and cladding. In this case, the largest modulus of elasticity equals 5794 MPa. The lowest modulus of elasticity 761 MPa characterized panels with perpendicular orientation of the core and cladding. The highest specific absorption energy was characterized by a beam type of TcLf 54.4 J/kg. It has been numerically shown that for the YX direction, increasing the auxetic properties of the core raises the panel's modulus of elasticity and amount of energy absorption. In the opposite direction, XY, increasing the auxetic properties of the core raises the panel's modulus of elasticity and slightly decreases the energy absorbed. The compiled values of RJS < 5 % classify the obtained panels as structures with negligible core stiffness. At the same time, this means that the samples should have significant lengths, several times longer than those used in the tests. Last but not least, it is worth to stress that the results of present studies indicate that lower values of Poisson's ratio, and therefore better auxetic properties of the panels, slightly reduce their elastic moduli, which is in contrast to all previous scientific reports known to the authors.