Territorial space (TS) is multifunctional, and exploring the relationships between functions and their influencing factors is key to achieving sustainable development of territorial space. However, existing research mostly focuses on the exploration of administrative units, while the exploration of grid units needs to be improved. This paper takes the Beibu Gulf Economic Zone (BGEZ) in Guangxi as the research object, evaluates the “Production–Living–Ecological” Functions (PLEFs) of territorial space using the land category scoring method and summarizes the evolution characteristics of its spatial pattern. It analyzes the dominant and combined functions of territorial space using the revealed comparative advantage index, explores the relationships between various functions by introducing a coupling coordination degree model, and comprehensively uses Geodetector and Geographically and Temporally Weighted Regression (GTWR) models to analyze the spatiotemporal heterogeneity of influencing factors on the coupling coordination degree of functions. The results indicate that at the grid scale (1) regional territorial space is dominated by ecological space, followed by production space, with living space accounting for the smallest proportion. Production space and ecological space has decreased, while living space has increased, with production and ecological spaces mostly flowing into living space. (2) The spatial distribution of production and ecological functions is relatively homogeneous, while the spatial differentiation of living functions is most significant. The grid can be divided into three function-dominant types and six function-combination types. (3) Living function is primarily disordered with production and ecological functions, while production–ecological function is mainly coordinated. (4) Policy regulation is a key factor affecting the degree of functional coordination, and the degree and scope of influence of each factor show significant spatiotemporal heterogeneity. This study reveals the functional relationships and the mechanisms of temporal and spatial evolution of TS at the grid scale, providing a scientific basis for the efficient and sustainable use of TS.

Territorial Space (TS) is characterized by its multifunctionality. The identification and management of Territorial Spatial Functions (TSFs) across multi-scale is crucial for achieving the SDGs. However, previous studies have primarily concentrated on the variations in TSFs within the administrative or grid units at a single scale, with multi-scale investigations remaining a challenge. This study focuses on the typical karst region of Guangxi province in China and develops a Multi-Scale Fusion model (MSF) for assessing TSFs and employs a coupling coordination degree (CCD) model to examine the TSFs relationships. Furthermore, principal component analysis (PCA) is used to classify various types of influencing factors, and the Revealed Comparative Advantage (RCA) index is employed to identify the primary types of influencing factors at the county level. The study integrates coupling coordination types and advantage factors into the zoning process. The results demonstrate: (1) Ecological function is the dominant function. At the administrative unit scale, production and living functions exhibit a spatial pattern of “high in the southeast and low in the northwest”, while ecological function shows the opposite pattern. Under grid units scale and multi-scale fusion, the high and low texture characteristics of production and ecological functions are more pronounced. (2) TSFs are primarily characterized by slight and moderate disorder. Slight disorder is widely distributed, while moderate disorder is predominantly found in the northwest karst mountainous regions. In contrast, coordinated relationships are more frequently observed in urban areas. (3) The driver types of TSFs can be categorized into four categories: Terrain-Population, Agriculture Development, Location-Economy, and Non-Agriculture Development. By integrating the TSFs relationships, six zones are delineated. Based on this, precise and differentiated optimization suggestions are proposed to promote orderly utilization and sustainable development of TS.