The blockage and alteration of wettability in reservoirs caused by asphaltene deposits are problems that contribute to poor oil recovery performance during carbon dioxide (CO2) injection. Oil production and reservoir damage are both controlled by macroscopic interlayer heterogeneity and microscopic pore-throat structure and may be optimized by the choice of flooding method. In this work, the residual oil distribution and the permeability decline caused by organic and inorganic precipitation after miscible CO2 flooding and water-alternating-CO2 (CO2-WAG) flooding have been studied by carrying out core-flooding experiments on a model heterogeneous three-layer reservoir. For CO2, flooding experimental results indicate that the low-permeability layers retain a large oil production potential even in the late stages of production, while the permeability decline due to formation damage is larger in the high-permeability layer. We found that CO2-WAG can reduce the influence of heterogeneity on the oil production, but it results in more serious reservoir damage, with permeability decline caused by CO2–brine–rock interactions becoming significant. In addition, miscible CO2 flooding has been carried out for rocks with similar permeabilities but different wettabilities and different pore-throat microstructures in order to study the effects of wettability and pore-throat microstructure on formation damage. Reservoir rocks with smaller pore-throat sizes and more heterogeneous pore-throat microstructures were found to be more sensitive to asphaltene precipitation, with corresponding lower oil recovery and greater decreases in permeability. However, it was found that the degree of water wetness for cores with larger, more connected pore-throat microstructures became weaker due to asphaltene precipitation to pore surfaces. Decreasing the degree of water wetness was found to be exacerbated by increases in the sweep volume of injected CO2 that arise from cores with larger and better connected pore throats. Erosion of water wetness is a disadvantage for enhanced oil recovery operations as asphaltene precipitation prevention and control measures become more necessary.