Integrating carbon capture and storage (CCS) technology into an integrated energy system (IES) can reduce its carbon emissions and enhance its low-carbon performance. However, the full CCS of flue gas displays a strong coupling between lean and rich liquor as carbon dioxide liquid absorbents. Its integration into IESs with a high penetration level of renewables results in insufficient flexibility and renewable curtailment. In addition, integrating split-flow CCS of flue gas facilitates a short capture time, giving priority to renewable energy. To address these limitations, this paper develops a carbon capture, utilization, and storage (CCUS) method, into which storage tanks for lean and rich liquor and a two-stage power-to-gas (P2G) system with multiple utilizations of hydrogen including a fuel cell and a hydrogen-blended CHP unit are introduced. The CCUS is integrated into an IES to build an electricity–heat–hydrogen–gas IES. Accordingly, a deep low-carbon economic optimization strategy for this IES, which considers stepwise carbon trading, coal consumption, renewable curtailment penalties, and gas purchasing costs, is proposed. The effects of CCUS, the two-stage P2G system, and stepwise carbon trading on the performance of this IES are analyzed through a case-comparative analysis. The results show that the proposed method allows for a significant reduction in both carbon emissions and total operational costs. It outperforms the IES without CCUS with an 8.8% cost reduction and a 70.11% reduction in carbon emissions. Compared to the IES integrating full CCS, the proposed method yields reductions of 6.5% in costs and 24.7% in emissions. Furthermore, the addition of a two-stage P2G system with multiple utilizations of hydrogen further amplifies these benefits, cutting costs by 13.97% and emissions by 12.32%. In addition, integrating CCUS into IESs enables the full consumption of renewables and expands hydrogen utilization, and the renewable consumption proportion in IESs can reach 69.23%.