Escalating geopolitical risks are one of the defining characteristics of the profound global changes underway. Investigating the impact of geopolitical risks on economic growth and their underlying mechanisms is crucial for understanding the political-economic nexus and improving national risk management strategies. Within the framework of an extended quantile model, this paper analyzes the effects of geopolitical risks on the probability distribution and term structure of China"s economic growth. The results reveal three key findings: First, geopolitical risks significantly alter the probability distribution of China"s economic growth, skewing it to the left and increasing the likelihood of economic downturns. Traditional mean-based models underestimate the negative impact of geopolitical risks, while quantile-based models more accurately capture the tail risks, particularly showing that the negative effects are primarily realized through an increased probability of left-tail outcomes. Second, growth-at-risk is event-driven, with major geopolitical conflict events leading to a substantial downward shift in the growth-at-risk position, heightening economic uncertainty and vulnerability to downturns. These negative impacts are not short-lived but exhibit both lagging and persistent effects. Third, the mechanisms through which geopolitical risks affect economic growth are multifaceted, including weakening market confidence, increasing policy uncertainty, causing stock market declines, credit contractions, and negatively affecting trade. These findings provide a basis for understanding the economic consequences of geopolitical risks and formulating appropriate countermeasures. Consequently, stabilizing growth and mitigating risks must prioritize geopolitical risks as a key concern.