Due to growing environmental issues, research on carbon dioxide (CO2) use is widely conducted and efforts are being made to produce useful materials from biomass-derived resources. However, polymer materials developed by a combined strategy (i.e., both CO2-immobilized and biomass-derived) are rare. In this study, we synthesized biomass-derived poly(carbonate-co-urethane) (PCU) networks using CO2-immobilized furan carbonate diols (FCDs) via an ecofriendly method. The synthesis of FCDs was performed by directly introducing CO2 into a biomass-derived 2,5-bis(hydroxymethyl)furan. Using mechanochemical synthesis (ball-milling), the PCU networks were effortlessly prepared from FCDs, erythritol, and diisocyanate, which were then hot-pressed into films. The thermal and thermomechanical properties of the PCU networks were thoroughly characterized by thermogravimetric analysis, differential scanning calorimetry, dynamic (thermal) mechanical analysis, and using a rheometer. The self-healing and recyclable properties of the PCU films were successfully demonstrated using dynamic covalent bonds. Interestingly, transcarbamoylation (urethane exchange) occurred preferentially as opposed to transcarbonation (carbonate exchange). We believe our approach presents an efficient means for producing sustainable polyurethane copolymers using biomass-derived and CO2-immobilized diols.