To promote low-carbon transformation and achieve carbon peak and neutrality in the energy field, this study proposes an operational optimization model considering the energy- and load-side dual response (ELDR) mechanism for electrothermal coupled virtual power plants (VPPs) containing a carbon capture device. The organic Rankine cycle (ORC) waste heat boiler (WHB) is introduced on the energy side. The integrated demand response (IDR) of electricity and heat is performed on the load side based on comprehensive user satisfaction (CUS), and the carbon capture system (CCS) is used as a flexible resource. Additionally, a carbon capture device operation mode that makes full use of new energy and the valley power of the power grid is proposed. To minimize the total cost, an optimal scheduling model of virtual power plants under ladder-type carbon trading is constructed, and opportunity-constrained planning based on sequence operation is used to address the uncertainty problems of new energy output and load demand. The results show that the application of the ELDR mechanism can save 27.46% of the total operating cost and reduce CO₂ emissions by 45.28%, which effectively improves the economy and low carbon of VPPs. In particular, the application of a CCS in VPPs contributes to reducing the carbon footprint of the system.