As climate change intensifies, surface vegetation productivity and carbon exchange between terrestrial ecosystems and the atmosphere are significantly affected by the variation of climatic factors. Due to the sensitivity of grasslands to these climatic factors, it is crucial to understand the response of vegetation greenness, or carbon exchange within grasslands, to environment factor dynamics. In this study, we used solar-induced chlorophyll fluorescence (SIF), precipitation (P), vapor pressure deficit (VPD), evaporative stress (ES), and root zone soil moisture (RSM) derived from remote sensing, reanalysis, and assimilation datasets to explore the response of vegetation greenness within Eurasian Steppe to climatic factors. Our results indicated deseasonlization based on the Seasonal-Trend decomposition using Loess (STL) method, which was an effective means to remove the seasonality disturbances that affect the qualification of the relationship between SIF and the four climatic factors. The response of SIF had a time lag effect on these climatic factors, and the longer the response period, the greater the impact on the correlation of SIF with P, VPD, ES, and RSM. We also found, among the four factors, that the response of SIF to ES was the timeliest. The findings of this study emphasized the impact of the seasonality and time lag effect on the dynamic response between variables, and provided references to the attribution and monitoring of vegetation greenness and ecosystem productivity.