The increasing severity of the effects of anthropogenic climate change, especially strengthening extreme events and wildfires, is motivating serious consideration of approaches for deliberate climate intervention. Stratospheric aerosol intervention (SAI), accomplished through direct injection of sulfur into the lower stratosphere, is considered the most feasible scheme that would have a significant impact on surface temperature. However, there are large uncertainties in the effects of SAI on terrestrial and marine ecosystems and their carbon sink strength, especially in the context of future negative emissions with carbon dioxide removal (CDR). To quantify the effects of SAI, especially when atmospheric CO2 concentration decreases due to strong CDR, the compound effects of CDR and SAI on the Earth’s climate and combined carbon sink strengths, we performed simulations of the ScenarioMIP SSP5-3.4-Overshoot (OS) scenario and a peak-shaving scenario using the Energy Exascale Earth System Model (E3SM) model. The peak-shaving scenario is a scenario in which SAI is applied under SSP5-3.4-OS to maintain its global mean surface air temperature less than 1.5 or 2.0^oC above the pre-industrial level. We also compared the simulations with those of CESM2-WACCM. Our results show that compared to SSP5-3.4-OS, the SAI induces more terrestrial carbon uptake, i.e., cumulative net biome production (cNBP) since 2040 under the peak-shaving 2.0^oC scenario, reaching a maximum of 61 PgC in 2079 and 43 PgC in 2100, while for CESM2, the cNBP continues to increase until reaching 24 PgC around 2100. The cNBP in 2100 differs considerably between E3SM and CESM2 in the boreal region, Amazonia, central and southern Africa, and southeastern Asia. The enhanced terrestrial cNBP is mainly due to large decreases in heterotrophic respiration (HR) for E3SM. However, it is caused by slight increases in Net Primary Production (NPP) and decreases in Heterotrophic Respiration (HR), respectively, for CESM2-WACCM.