Polynyas, as ice-free areas surrounded by thick sea-ice, are the most active hotspots of primary productivity and critical carbon sinks around Antarctica, as well as the main sources of Dense Shelf Water (DSW). Previous studies have generally assumed that the cross-slope transport of dense water can carry atmospherically derived carbon into the abyss, enabling carbon sequestration. However, this hypothesis has long lacked support from direct observational or modeling evidence. In this study, we employ a high-resolution MITgcm-Darwin coupled ocean-sea ice-ecosystem model to reproduce the biogeochemical cycling characteristics of the Cape Darnley polynya, and isolate the contribution of biological processes to the carbon cycling. Our results show that the air-sea carbon flux in the Cape Darnley Polynya region reaches 0.54 Tg C yr^-1, with the biological pump dominating this process (0.37 Tg C yr^-1). Most of the carbon entering the ocean via the local biological pump sinks to sediments, and only one quarter has the potential to reach the deep ocean. The seasonal mismatch between phytoplankton blooms and DSW formation is the primary cause of this pattern.