Large Igneous Province (LIP) eruptions are thought to have driven environmental and climate change over wide temporal scales ranging from a few to thousands of years. Since the radiative effects and atmospheric lifetime of carbon dioxide (CO2, warming) and sulfur dioxide (SO2, cooling) are very different, the conventional assumption has been to analyze the effects of CO2 and SO2 emissions separately and add them together a posteriori. In this study, we explore the complex and interconnected effects of volcanic gas emissions from LIPs on the ocean-atmosphere system and biosphere by analyzing the joint effect of CO2 and SO2 using a biogeochemical carbon cycle box model (LOSCAR). Using a range of volcanic gas forcings as well as models with and without volcanic SO2 emissions, we find that sulfur emissions have significant long-term (>1000 years) effects on the marine carbon cycle (dissolved inorganic carbon, pH, alkalinity, and carbonate compensation depth). This is due to two processes: the strongly temperature-dependent equilibrium coefficients for marine carbonate chemistry and the few 1000 year timescale for ocean overturning circulation. Thus, the effects of volcanic sulfur are not simply additive to the impact of carbon emissions. We also develop a causal mechanistic framework to understand and visualize the impacts of combined carbon and sulfur emissions, focusing on determining the feedback amplitudes and characteristic timescales. Our results underscore the critical need to unravel the complex feedback mechanisms within the Earth system to understand the diverse environmental responses triggered by large-scale volcanism over geological time scales.