Apart from the inherent anomalous behaviour under tensile and compressive structures, auxetic structures have shown improved energy absorption characteristics that are of prime interest to various fields of study. This is further exemplified by additive manufacturing (AM) techniques and polymer composites to tailor the shape, geometry and form of these structures. Consequently, this paper aims to characterise the in-plane compressive behaviour and negative Poisson’s ratio (NPR) of the most prominent auxetic structures fabricated additively used polymer nanocomposite materials. The study incorporates the use of glycol-modified polyethylene terephthalate (PETG) and nanocomposites of PETG filled with organically modified montmorillonite (OMMT) nanoclay particles to produce auxetic structures fabricated through fused filament fabrication (FFF). Different structures such as hexagonal re-entrant honeycomb structures, peanut-shaped honeycombs, chiral honeycomb structures and missing rib structures are characterised for their compressive performance through experimental approaches involving mechanical testing and digital image correlation (DIC). Different parameters such as the peak crushing strength, average crushing strength, NPR, specific energy absorption (SEA), and crush force efficiency (CFE) of these structures are evaluated at different strain rates/loading rates for varying concentrations of nanoclay and PETG. It is observed that higher loadings of nanoclay particles lower the compressive strength of the structures. Additionally, the NPR decreases with increasing strain rates and is also influenced by the composition and the resultant stiffness. Moreover, the geometrical parameters of the structure largely influence its strain energy absorption. The results have shown that such material-structure combinations can produce structures of high-performance capabilities suitable for aerospace applications.