Understanding the relationships among multiple territorial space functions and their influencing factors is of great significance to achieve the sustainable development and protection of territorial space. By taking the Beijing-Tianjin-Hebei region as a case study area, this study explored the spatio-temporal evolution process of multiple territorial space functions at the grid scale by assimilating datasets from multiple sources. Then, the trade-offs and synergy among multiple territorial space functions were identified by Spearman correlation analysis and root mean squared error (RMSE). Furthermore, geographic detector model was applied to explore influencing factors associated with the trade-off intensity of territorial space functions. The results revealed that the high value areas of production function and living function were mainly concentrated in the southeastern area, while the ecological function in the northwestern area was higher. In terms of temporal evolution, the results showed a trend of increasing grain production, non-agricultural production, living maintenance, residential support and water conservation, but decreasing carbon storage, soil conservation and habitat quality from 2000 to 2020. Additionally, the Beijing-Tianjin-Hebei region has the highest trade-off intensity between living function and ecological function, followed by production function and ecological function, and the lowest trade-off intensity between production function and living function. During 2000 and 2020, the trade-off intensity between living function and ecological function slightly weakened from 0.206 to 0.205, and the trade-off intensity between production function and ecological function weakened from 0.190 to 0.180. However, the trade-off intensity between production function and living function increased from 0.038 to 0.060. The strong trade-off intensity between living function and ecological function, as well as between living function and ecological function, primarily occurred in the northwest of Beijing-Tianjin-Hebei region, especially in Chengde, Qinhuangdao, and Beijing. The southeastern plains area was the main agglomeration area with strong trade-off intensity between production function and living function, especially in Hengshui, Handan and Xingtai. The natural factors, land use factors, and socioeconomic factors were the common factors affecting the spatial differentiation of multifunctional trade-off intensity. Land use factors, especially land use intensity, had the greatest impacts on the trade-offs among multiple territorial space functions. The influence intensity of each factor is slightly different in different years. Policymakers are suggested to optimize the territorial space development and protection pattern by coordinating territorial space composite functions. Thus, the results of this study provide a quantitative reference and policy decision basis to help mitigate conflicts and further improve the harmonization of territorial space.