Photopolymerization is the governing chemical mechanism in two-photon lithography, a multi-step additive manufacturing process. Negative-tone photoresist materials are widely used in this process, enabling the fabrication of structures with nano- and micro-sized features. The present work establishes the relationship among the process parameters, the degree of polymerization, and the nonlinear stress-strain response of polymer structures obtained through two-photon polymerization. Honeycomb structures are fabricated on a direct laser writing system (Nanoscribe) making use of different laser powers for two widely applicable, commercially available resins (IP-S and IP-Dip). The structures are then tested under uniaxial compression to obtain the corresponding stress-strain curves up to 30% strain. Raman spectroscopy is used to correlate the degree of conversion achieved upon different laser exposures of the base photoresist material with the selected mechanical properties (Young’s modulus, tangent modulus, deformation resistance) after polymerization. Significant differences are recorded in the observed constitutive responses. Higher degrees of conversion result in higher elastic moduli and strength at large strains. Moreover, it is found that the IP-Dip resin yields higher degrees of conversion for the same laser power compared to the IP-S resin. A neural network model is developed for each resin that predicts the stress-strain response as a function of the degree of conversion. For each material, an analytical form of the identified constitutive response is provided, furnishing basic formulas for engineering practice.