Future networks demand ubiquitous and interconnected information services in a full-dimensional space. However, the infrastructure and the deriving technology system of the existing satellite Internet still face unprecedented challenges in terms of heterogeneous collaboration, resource efficiency, precision on demand, stability, and reliability. In this article, we analyze the development demand for satellite Internet in China and discuss the development status and trend of satellite Internet worldwide. Subsequently, we elaborate on a typical space–ground cooperative networking architecture and full-dimension definable network nodes. Ultimately, we propose the key intelligent-slicing technologies for a space–ground cooperative network in terms of network intelligent slicing, data analysis and forwarding, and the resource coordination and control mechanism. Furthermore, a development route is proposed for the intelligent slicing technology. Breakthroughs should be made on key technologies such as the businesson-demand intelligent slicing, data analysis and forwarding with full-dimension definability, and the global source coordination and control technologies; these breakthroughs should rely on the space–ground cooperative network architecture and supported by technologies such as network resource management and control, network intelligence, and full-dimension definability of the network architecture. This will ultimately provide continuous impetus for the innovation of the global dynamic optimization technology of the space–ground cooperative network resources.