The “dual-carbon” goal puts forward higher requirements for green development, and green finance plays an important role in promoting green economic transformation and realizing the “dual-carbon” goal. However, existing empirical studies mainly focus on the impact of green finance on carbon peaking (carbon emission reduction effect). There are few empirical analyses on green finance enabling carbon neutrality from the dimensions of carbon reduction and carbon removal, and there is a lack of testing of the corresponding spatial effects. This paper believes that green finance will direct social capital to productive activities that are conducive to green development and lead to more resources being allocated to pollution control and environmental protection. This will reduce the amount of carbon emitted per unit of output and enhance regional carbon removal capacity, thereby contributing to carbon neutrality. To be specific, the development of green finance is conducive to the increase of energy saving and emission reduction input in economic activities and the clean energy consumption structure, so as to enable carbon neutrality from the dimension of carbon emission reduction. It is beneficial to improve the terrestrial carbon sink capacity through green agriculture and forestry development, and thus to enable carbon neutrality from the carbon removal dimension. It is conducive to promoting the innovation and application of green technology, promoting the low-carbon and ecological transformation of industrial structure and foreign investment structure, and thus enabling carbon neutrality from the dimensions of carbon reduction and carbon removal. Meanwhile, under the spatial spillover effect of green finance development, carbon emission and carbon removal, green finance enabling carbon neutrality have a spatial spillover effect. The dynamic SDM model was used to analyze 30 sample regions in China from 2010 to 2020, and it was found that both the level of green financial development and the level of carbon deficit have significant spatial autocorrelation; the improvement of regional green finance development level is conducive to local carbon emission reduction and carbon removal, thus reducing the local carbon deficit level, as well as the carbon emission and carbon deficit level of neighboring regions; in general, the direct effect of green finance on carbon neutrality is greater than the indirect effect, and the short-term effect is greater than the long-term effect; in addition, increased expenditure on energy conservation and environmental protection, clean energy consumption structure, and industrial structure upgrading can inhibit the increase of carbon emissions, the improvement of forest coverage can promote the increase of carbon removal, and the innovation and application of green technology can promote carbon reduction and carbon removal. Compared with existing literature, this paper mainly expands and deepens this study as follows: firstly, the conduction mechanism of green finance enabling carbon neutrality is systematically discussed in theory; secondly, carbon deficit, carbon reduction, and carbon removal are included in the same analytical framework to test the promoting effect of green finance development on carbon neutrality and its spatial spillover effect. This study shows that green finance development will not only help achieve local carbon neutrality, but also have positive spatial spillover effects on neighboring areas. It is necessary to further tap and enhance the positive effects of green finance development, strengthen its guiding role in capital flow, strengthen green regulation, and focus on solving problems such as insufficient investment in green technology innovation and misallocation of green resources. In particular, it is necessary to pay attention to and avoid the negative impact of the “greenwashing” phenomenon.