The proposed carbon-neutral and carbon-peak targets will help China achieve a low-carbon economic transition and embark on a high-quality development path. As the developing country with the highest carbon emissions, the path to energy conservation and emission reduction will be long and difficult. Given the current complex international situation, which includes high geopolitical risks and frequent internal policy adjustments, this paper empirically investigates the time-varying effects of political uncertainty risks on China's carbon emission intensity over time and at equal intervals from 1995 to 2020 using the TVP-VAR model and the research objects of geopolitical risks, economic policy uncertainty risks, and carbon emission intensity. The empirical findings show that both geopolitical risk and economic policy uncertainty significantly increase carbon emission intensity, and the impact of geopolitical risk tends to expand gradually, despite abrupt structural changes in different time periods, which should be emphasized. Meanwhile, the article investigates the possible paths of political risks impeding the achievement of the dual-carbon target from the perspectives of R&D investment and science and technology innovation and makes a series of policy recommendations as a result.