Crosslinked polyhydroxyurethane (PHU) networks synthesized from difunctional six‐membered cyclic carbonates and triamines are reprocessable at elevated temperatures through transcarbamoylation reactions. Here we study the structural effects on reprocessability and stress relaxation in crosslinked PHUs. Crosslinked PHUs derived from bis(five‐membered cyclic carbonates) are shown to decompose at temperatures needed for reprocessing, likely via initial reversion of the PHU linkage and subsequent side reactions of the liberated amine and cyclic carbonate. Therefore, several six‐membered cyclic carbonate‐based PHUs with varying polymer backbones and crosslink densities were synthesized. These networks show large differences in the Arrhenius activation energy of stress relaxation (from 99 to 136 kJ/mol) that depend on the network structure, suggesting that transcarbamoylation reactions may be highly affected by both chemical and mechanical effects. Furthermore, all crosslinked PHUs derived from six‐membered cyclic carbonates show mechanical properties typical of thermoset polymers, but recovered as much as 80% of their as‐synthesized tensile properties after elevated temperature compression molding. These studies provide significant insight into factors affecting the reprocessability of PHUs and inform design criteria for the future synthesis of sustainable and repairable crosslinked PHUs. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017, 134, 44984.