China has a high frequency of natural disasters and it has become the economy with the largest carbon emissions in recent years. In this study, we mainly investigated the relationships between carbon emissions and natural disaster losses in China, as well as considering important factors such as economic growth and new energy consumption. Time series data for China from 2000 to 2020 were selected and based on the nonlinear auto-regressive distributed lag model method, a short-term error correction model and long-term co-integration relationship model were obtained between carbon emissions and their related factors. The results showed that in the long run, there is a significant nonlinear relationship between carbon emissions, new energy consumption and direct economic losses from natural disasters. There is a significant U-shaped relationship between natural disasters and carbon emissions, that is, natural disaster losses will significantly inhibit carbon emissions before they are below a certain threshold, but fewer natural disaster losses will increase carbon emissions. On the contrary, there is an inverted U-shaped relationship between new energy consumption and carbon emissions. When new energy consumption exceeds a certain threshold, it will help carbon peak early. In the short term, the impact of natural disasters on carbon emissions in the current period is significantly positive and higher than that in the lagged period, but the impact of its square term is negative. The short-term error correction model coefficient is −0.6467, and the error will be corrected when the short-term volatility deviates from the long-term equilibrium. These results suggest that attention should be paid to reducing disaster losses and the low-carbon reconstruction path for natural disasters, as well as continuously improving the level of new energy utilization, accelerating the pace of energy substitution, and promoting economic transformation for achieving “carbon peaking” in China.