The increasing emission of anthropogenic greenhouse gasses, responsible for the rise in global mean surface temperature, poses severe threats to natural Earth systems. Mitigating this temperature increase through stratospheric aerosol intervention (SAI) has been suggested as one potential mitigation solution. However, the resulting climate alterations can have significant implications for photosynthetic activity and ecosystem health, subsequently modifying the terrestrial carbon cycle. Our research addresses the influence of such geoengineered climates on various aspects of the carbon cycle, with a particular focus on projected vegetation productivity under high radiative forcing scenarios like the Geoengineering Model Intercomparison Project (GeoMIP) G6 sulfur simulation experiment. Global gross primary productivity (GPP) and net biome productivity (NBP) exhibit increases under higher radiative forcing scenarios in many models as compared to lower radiative forcing scenarios. SAI is expected to impact not just the mean response on the carbon cycle, but also the intensity and frequency of extreme anomalies in photosynthesis, also called carbon cycle extremes, by altering vegetation productivity. We hypothesize that the magnitude of positive and negative carbon cycle extremes would be reduced under a low radiative forcing scenario relative to a high radiative forcing scenario. Our results suggest that SAI will reduce the intensity and frequency of negative carbon extreme events compared to high climate forcing scenarios. While most regions showed the reduction of extreme events under SAI along with increased productivity, especially in North America, Europe and northern part of Asia, parts of Australia and Central Africa showed losses in plant productivity consistent with increased negative carbon extremes. An important aspect of our research is to understand the climatic drivers of carbon cycle extremes, which include variations in temperature, precipitation, evaporation and solar radiation. By understanding these drivers, we aim to provide comprehensive insight into the potential impacts and effectiveness of geoengineering efforts. The results from this study are anticipated to contribute to understanding the impacts of geoengineering, specifically in relation to the carbon cycle.