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Spatio-temporal variation of climatic factors generally contains spatial and temporal components that have different frequencies, which may significantly affect the overall variance structure of vegetation growth at the original scale. The objective of the study was to explore the temporal- and spatial-scale-specific relationships between vegetation growth and climatic factors based on the data of half-monthly normalized difference vegetation index (NDVI), half-monthly averaged daily mean temperature (DMT), half-monthly averaged daily range of temperature (DRT), and half-monthly accumulated precipitation (AP). The complete ensemble empirical mode decomposition (CEEMD) was used to decompose the temporal series of NDVI and climatic factors, and their temporal-scale-specific relationships were examined based on the original half-month scale. Two-dimensional empirical mode decomposition (2D-EMD) was used to decompose the spatial distributions of temporally averaged NDVI and climatic factors, and their spatial-scale-specific relationships were tested based on the original resolution of 1 km. The dominant temporal scales of NDVI were around 3, 15, and >15 years, while the dominant spatial scales of NDVI were around 2 × 104 and >10 × 104 km2. The temporal-scale-specific effects of climatic factors on NDVI were the strongest under mixed forest and were the weakest under broadleaf forest. On a 15-year time scale, NDVI was positively affected by DMT and AP at the 200–1,000 mm precipitation region and negatively affected by DRT at the 200–600 mm precipitation region. Temporal effects of climatic factors had the greatest effects on NDVI in the precipitation region of 200–600 mm and in Yunnan province, and 98.08% of the study area included multi-temporal scale effects. Relationships between NDVI and climatic factors at the half-month scale and other temporal scales were different under different elevation, latitude, longitude, land types, climatic regions, and precipitation. The spatial-scale-specific effects of climatic factors on NDVI were also differed, and the area with effects of the multi-spatial scale was about 64.38%. This indicated that multi-temporal scale and multi-spatial scale analysis could help to understand the mechanisms of effect of climatic factors on vegetation growth and provide the foundation for future vegetation restoration in fragile ecosystems.