Poverty eradication is a crucial element of SDG 1. Whether the financial resources invested by the Government provide a critical impetus for deeply impoverished rural areas needs to be studied by quantitative analysis. Therefore, this study presents a theoretical analytical framework for agricultural production–government poverty reduction. It divides the poverty reduction process into two stages, agricultural production and poverty reduction, from the perspective of sustainable agricultural development. The comprehensive measurement and spatio-temporal evolution analysis of China’s agricultural production and poverty reduction efficiency are conducted using a novel dynamic two-stage DEA model, which incorporates non-expected factors. The study found that (1) China’s agricultural production and poverty reduction efficiency exhibit overall poor performance, characterized by two poles of differentiation. (2) The agricultural production efficiency score is higher in the northern region than in the southern region, while the poverty reduction efficiency score is higher in the eastern region compared to the western region. (3) The coupling and coordination between China’s production efficiency and poverty reduction efficiency are inadequate.