This paper aims to examine whether country-level climate risk influences carbon emissions by companies. It also investigates how financial slack shapes firms' responses to climate risk. Based on country-level climate risk index from Germanwatch from 2010 to 2019, the results show that climate risk negatively affects carbon emissions. This result suggests that companies operating in countries that face extreme weather events are exposed to high institutional pressures, leading them to adapt to climate change by engaging in activities that reduce carbon emissions. The results also show that firms with available slack better respond to such climate challenges, given the internal resources available to finance carbon reduction investments. We also find that after the Paris Agreement on Climate Change in 2015, firms facing greater climate risk have actively reduced their carbon emissions to converge with carbon neutrality goals. Further analyses show that this negative effect is exacerbated for companies with strong corporate governance and high environmental performance and for those operating in intensively polluted industries. Our results are robust to several checks, including alternative measures and endogeneity concerns.