Poverty caused by disasters poses a great challenge to consolidate the achievements of poverty alleviation. Livelihood resilience is the key factor for farmers to resist risks and get rid of poverty. Therefore, this study used the China Family Panel Studies (CFPS) database. Firstly, we examined the impact of natural disasters on the poverty vulnerability of farmers. Secondly, taking livelihood resilience and its decomposition dimensions as threshold variables, we examined the mechanism of livelihood resilience between natural disasters and poverty. The results show that natural disaster shocks, natural disaster intensity, and natural disaster frequency all had a significant positive effect on farm households’ vulnerability to poverty. The threshold test shows that natural disasters had larger effects on the poverty vulnerability of the farmers with lower buffer capacity, self-organizing capacity, and learning capacity. When the livelihood resilience value exceeded the third threshold, the impact of natural disasters on the poverty vulnerability of farmers turned from positive to negative. When the buffer capacity exceeded the third threshold, the impact of natural disasters on poverty vulnerability turned from positive to negative; when the self-organizing capacity exceeded the first threshold, the impact of natural disasters on poverty vulnerability turned from positive to negative; when the learning capacity exceeded the third threshold, the impact of natural disasters on poverty vulnerability turned from positive to negative. Therefore, it is suggested that appropriate policies should be needed to support farmers’ livelihood resilience and address disaster-induced poverty by improving farmers’ buffer capacity, self-organizing capacity, and learning capacity. Focusing on farmers’ livelihood resilience, government should establish a policy support system aimed at improving farmers’ buffer capacity, self-organizing capacity, and learning capacity, that will help farmers to escape from disaster-induced poverty.