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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, was used to produce such specimens. Residual stress (RS) and warpage, more or less, always exist in such specimens due to their layer-by-layer fabrication, i.e., repeated heating and cooling. The RS influences the auxetic deformation behavior, but its measurement is challenging due to its very fine structure. Instead, the finite-element (FE)-based process simulation realized using an ABAQUS plug-in numerically predicts the RS and warpage. The predicted warpage shows a negligibly slight deviation compared to the design topology. This process simulation also provides the temperature evolution of a small-volume material, revealing the effects of 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 consideration of the RS, 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 the evolution, where the first three and the warpage are also compared with the experimental results. Furthermore, the FE simulation can easily provide the global stress–strain flow curve with the total stress calculated from the elemental stresses.