The slowdown of the Atlantic Meridional Overturning Circulation (AMOC) and its consequences on ocean carbon uptake have significant implications for the Earth's climate system and the global carbon cycle. This study analyzes ten Earth System Models from the Coupled Model Intercomparison Project Phase 6 (CMIP6) and reveals a moderate correlation between the regional carbon uptake in the subpolar North Atlantic and the decline in AMOC at 40°N under a high CO₂ emission scenario. AMOC transports warm and salty subtropical waters to the subpolar regions, and models with a stronger AMOC slowdown generally exhibit weaker surface warming and larger declines in surface salinity and alkalinity. We investigate two plausible mechanisms linking the AMOC slowdown to the decline of regional CO₂ uptake: the reduction in surface alkalinity and diminished subduction. The decline in surface salinity and alkalinity reduces the ocean's capacity to buffer acids, leading to a reduced CO₂ uptake, a phenomenon unique to the North Atlantic. Additionally, as shown in previous research, diminished convective mixing and surface water subduction further decrease the downward transport of anthropogenic carbon. Centennial trends of partial pressure of CO₂ (pCO₂) are decomposed into four components driven by temperature, salinity, alkalinity, and dissolved inorganic carbon, highlighting that both alkalinity and dissolved inorganic carbon are significant contributors. The alkalinity-driven pCO₂ essentially follows surface salinity, establishing the linkage between AMOC slowdown and alkalinity decline. Our results indicate that changes in alkalinity are crucial for understanding the interplay between AMOC and regional carbon sequestration abilities across the late 20^th and the 21^st centuries in the subpolar North Atlantic. This study underscores the importance of considering AMOC dynamics in future projections of ocean carbon uptake and climate change impacts.