Carbon geosequestration mitigates the consequences of high concentrations of carbon dioxide (CO2) in the atmosphere by capturing and safely disposing of CO2 into various geological formations, viz., deep saline aquifers. The long-term fate of CO2 in host aquifers depends on the sealing efficiency of the caprock. Some caprocks are rich in clay minerals, having the potential to adsorb CO2 and swell under reservoir conditions. However, the role of CO2-clay interaction, specifically adsorption-induced strain, in altering the sealing efficacy of the caprock at reservoir conditions is unknown. This research investigates the long-term behaviour, including stress state and failure mechanism, of clay-rich caprock when exposed to CO2 under typical reservoir conditions using a coupled two-phase hydromechanical model. The study revealed that the interaction between CO2 and clay affects the stress state and failure type, depending on the stress ratio and saturation pressure. Unmonitored CO2 injection can lead to slip and hydraulic failure, with failure onset varying across the thickness of the clay-rich medium. Additionally, the effect of moisture content on the stress state and permeability of the clay-rich caprock is examined. It is revealed that the mean effective stress and shear stress at different moisture content depends on the changes in the injection pressure. When CO2 injection is performed at increasing pressure, shear stress is observed to decrease, unlike mean effective stress owing to strain redistribution. The reduction in the porosity due to clay particle swelling is moderated by poroelastic and suction-induced strains, with the latter having a significant impact. This intricate interplay of strains suggests a potential increase in CO2 storage capacity. The research highlights the complex hydromechanical interactions between CO2, water, and clay minerals, showing how poroelastic and CO2 adsorption influences porosity and stress states and underscores the importance of suction-induced strain in optimizing CO2 storage.