In recent years, the accelerated pace of urbanization has increased patch fragmentation, which has had a certain impact on the structure and ecological environment of forest–grass ecological networks, and certain protection measures have been taken in various regions. Therefore, studying the spatiotemporal changes and correlations of ecological service functions and forest–grass ecological networks can help to better grasp the changes in landscape ecological structure and function. This paper takes the Wuding River Basin as the research area and uses the windbreak and sand fixation service capacity index, soil conservation capacity, and net primary productivity (NPP) to evaluate the ecological service capacity of the research area from the three dimensions of windbreak and sand fixation, soil conservation, and carbon sequestration. The Regional Sustainability and Environment Index (RSEI) is used to extract ecological source areas, and GIS spatial analysis and the minimum cumulative resistance (MCR) model are used to extract potential ecological corridors. Referring to complex network theory, topology metrics such as degree distribution and clustering coefficient are calculated, and their correlation with ecological service capacity is explored. The results show that the overall ecological service capacity of sand fixation, soil fixation, and carbon sequestration in the research area in 2020 has increased compared to 2000, and the ecological flow at the northern and northwest boundaries of the river basin has been enhanced, but there are still shortcomings such as fragmented ecological nodes, a low degree of clustering, and poor connectivity. In terms of the correlation between topology indicators and ecological service functions, the windbreak and sand fixation service capacity index have the strongest correlation with clustering and the largest grasp, while the correlation between soil conservation capacity and eigencentrality is the strongest and has the largest grasp. The correlation between NPP and other indicators is not obvious, and its correlation with eccentricity and eigencentrality is relatively large.