Global warming, caused by the greenhouse effect, has triggered numerous unprecedented extreme weather events globally. Agricultural technology is the fundamental force that promotes the development of the agricultural industry. Studying the impact mechanism of agricultural technology on agricultural carbon emissions will help transform traditional agriculture into ecological, green, and low-carbon modern agriculture, and it is of great significance to the realization of carbon neutrality and carbon peaks. This study used panel data from 31 provinces and cities in China from 2001 to 2020. First, the stochastic frontier model was used to extend existing research from a broad and narrow sense of agricultural technical progress to agricultural technical efficiency. The total agricultural carbon emissions and intensity of agricultural carbon emissions were then calculated and compared. Finally, we constructed the spatial Dubin model and the threshold model with agricultural technical efficiency as the threshold variable, which revealed the spatial effect and non-linear relationship between agricultural technical efficiency and agricultural carbon emissions. The results showed that the total and intensity of agricultural carbon emissions had decreased in recent years. Central China had more agricultural carbon emissions than eastern and western China, and eastern China had a higher technical efficiency of agriculture and a lower carbon emission intensity of agriculture than central and western China. Agricultural carbon emission intensity and technical efficiency had spatial autocorrelation and agglomeration characteristics, and high-high clustering and low-low clustering are the main factors among the provinces. Agricultural carbon emission intensity had a positive spatial spillover effect on itself, but agricultural technical efficiency had a negative spatial spillover effect, which was conducive to the overall reduction of agricultural carbon emissions. Additionally, urbanization, human capital level, and per capita cultivated land area also had negative effects on agricultural carbon emission intensity, but the level of agricultural economic development and the degree of agricultural disaster had positive effects. There was a double threshold effect between agricultural technical efficiency and agricultural carbon emission intensity, which meant that when agricultural technical efficiency reached the “inflection point”, its impact on agricultural carbon emission intensity became negative, and after the level of agricultural technical efficiency was further improved, its influence weakened due to the diminishing marginal effect. Most existing research began with a broad or narrow definition of technological progress, but this study used technical efficiency as the research object after the decomposing technological progress in a broad sense, which further validated the indisputable and decisive role of technological progress in agricultural energy conservation and emission reduction. This study provides a theoretical and policy basis for exploring the path to achieving the “double carbon” goal.