The current work investigates the auxetic tensile deformation behavior of the inversehoneycomb structure with 5 × 5 cells made of biodegradable poly(butylene adipate-coterephthalate) (PBAT). Fused deposition modeling, an additive manufacturing method, produced such specimens. Residual stress (RS) and warpage, more or less, always exist in such specimens due to layer-by-layer fabrication, i.e., repeated heating and cooling. The RS influences the auxetic deformation behavior, but its measurement is challenging due to the very fine structure. Instead, the finite-element(FE)-based process simulation realized by an ABAQUS plug-in numerically predicts the RS and warpage. The predicted warpage shows a negligible slight deviation compared to the design topology. This process simulation also delivers the temperature evolution of a small volume material, revealing the local cyclic heating and cooling. The achieved RS serves as the initial condition for the FE model used to investigate the auxetic tensile behavior. With the outcomes from FE calculation without considering RS at hand, the effect of the RS on the deformation behavior is discussed for the global force-displacement curve, the structural Poisson’s ratio evolution, the deformed structural status, the stress distribution, and evolution, where the first three and the warpage are also compared with experimental results. Furthermore, the FE simulation can easily provide the global stress-strain flow curve with the total stress calculated from the elemental ones.