In the context of the "dual carbon" goal and high-quality development, promoting urban vitality and carbon reduction has become a key issue for sustainable urban development. Taking Fuzhou, a typical mountain and sea city, as an example, a six dimensional urban vitality evaluation system of "social economy culture space environment policy" is constructed based on multi-source data. Combined with carbon emission data, the township is taken as the basic unit, and bivariate spatial autocorrelation and optimal parameter geographic detector (OPGD) are used to reveal the spatial differentiation and driving path of urban vitality and carbon emissions. Research has found that: (1) Fuzhou city presents a hierarchical structure of "central high vitality - high carbon emissions agglomeration, peripheral low vitality - low carbon emissions", but policy driven new urban areas such as Changle Binhai New City have a jumping high-value area with "carbon emissions ahead of vitality", breaking the traditional hierarchical pattern; (2) Social, economic, cultural, spatial, and comprehensive vitality are significantly positively correlated with carbon emissions, while environmental and policy vitality are significantly negatively correlated with carbon emissions, indicating that ecosystems and policy interventions play a key regulatory role in carbon reduction; (3) The check-in density, functional mix, and GDP of Weibo are the core explanatory factors for the spatial heterogeneity of carbon emissions, and their interaction exhibits a nonlinear synergistic amplification effect; The total fishery production value and topographic index have a significant driving effect on carbon emissions, highlighting the uniqueness of mountain and sea cities. The research proposes strategies such as precise zoning regulation, coordinated governance of policies and environment, and building a resilient pattern of mountain sea synergy, providing scientific basis and decision-making reference for achieving synergy between vitality enhancement and carbon reduction in mountain sea cities.