Establishing a multi-objective development evaluation system for poverty-stricken households to realize the accurate identification and dynamic monitoring of relative poverty under different development goals has become an urgent need of poverty alleviation and development in the new stage of rural poverty alleviation. Taking into consideration the strategies of targeted poverty alleviation, rural revitalization, and sustainable development, this study designed a "goal fulfillment degree" Technique for Order Preference by Similarity to Ideal Solution (G-TOPSIS) multi-objective development evaluation model that reveals the development level and development gap of poverty-stricken households under the short-, medium-, and long-term goals, and detected the influencing factors of poverty reduction of farming households at different development levels based on geographical detector. Taking Fugong County, Yunnan Province as the study area, the results show that: 1) At present, there is a large number of farming households in the study area that are still in absolute poverty, and there is still a great pressure to tackle the poverty problem. Therefore, comprehensive poverty alleviation is the most urgent development goal of Fugong County. Farming households that are out of absolute poverty are still in relative poverty and have high poverty vulnerability. They are still far from the average development level of rural residents nation-wide and in the province. Therefore, the task of preventing and alleviating relative poverty in Fugong County is arduous. 2) Under the short-term goal, the main factors contributing to poverty are the number of years of education for the labor force, sanitary toilets, safe housing, per capita net income of the family, and family health; under the medium- and long-term goals, compared with the national and provincial levels, the main development weaknesses are per capita net income of the family, education for the labor force, and safe housing. 3) Affected by infrastructure, terrain, economic geographical location, natural resources, and traffic location, the spatial distribution characteristics of poor farming households at different development levels are very different. The lower the development level of farming households, the stronger the spatial heterogeneity, and the greater the impact of geographical environment. The research results can provide efficient technical decision-making support for the implementation of national precision poverty reduction strategies, rural revitalization strategies, and sustainable development strategies.