This paper demonstrates the molecular design of renewable polymer thermosets that are chemically recyclable yet degradable on demand. In this design, the thermosets comprise a limonene-based highly branched polymer, which has been synthesized via the regioselective thiol–ene reaction between natural limonene and multifunctional thiol, and a Meldrum’s acid derivative for the click/declick reaction of thiol groups that are deliberately positioned on the outer surface of the branched polymer. Thus, the accessible thiols expedite the covalent bond exchange reaction and enable the formation of a network and bulk recycling of the entire network; the labile cross-linkers enable molecular degradation or repurposing of the materials under benign conditions. The thermosets can be also reinforced with the addition of carbon fibers. Thus, reversible deformation or self-lamination of the resultant carbon composites, which are degradable and recyclable, was achieved owing to the thermosets, which act as a matrix or binder. We envision that the renewable materials presented here would be advanced by introducing diverse biomolecules or reversible chemistry to develop disposable bio-based platforms that can be further upcycled at the end of their lifecycles.