Despite significant past efforts to exploit green, renewable precursors in polymeric materials and to improve the recyclability and reprocessability of nonisocyanate polyurethane (NIPU) networks, no single study has previously investigated biobased polyhydroxyurethane (PHU) network reprocessability. Renewable, dynamic PHU networks were synthesized by reacting bioderived polyfunctional cyclic carbonates, carbonated soybean oil (CSBO), and sorbitol ether carbonate (SEC), with either a synthetic diamine or a biobased diamine. Network reprocessability was studied by dynamic mechanical analysis. With relatively mild reprocessing conditions, CSBO-based PHU networks exhibit complete recovery of crosslink density and associated properties after multiple melt-state recycling steps. In addition to the presence of reversible cyclic carbonate aminolysis and transcarbamoylation exchange reactions, CSBO-based networks were shown via a model reaction to undergo a third dynamic chemistry based on a transesterification exchange reaction. In contrast to the excellent property recovery achieved by CSBO-based PHU networks, as a result of disadvantageous monomer molecular design, SEC-based networks exhibit poor reprocessability even with increased catalyst load and reprocessing temperature and time. This work reveals the effect of monomer structure on the reprocessability of dynamic polymer networks and highlights the effectiveness of CSBO to serve as a precursor of robust, sustainable NIPU networks with excellent reprocessability.