Understanding the changing relationships between vegetation coverage and precipitation/temperature (P/T) and then exploring their potential drivers are highly necessary for ecosystem management under the backdrop of a changing environment. The Jing River Basin (JRB), a typical eco-environmentally vulnerable region of the Loess Plateau, was chosen to identify abrupt variations of the relationships between seasonal Normalized Difference Vegetation Index (NDVI) and P/T through a copula-based method. By considering the climatic/large-scale atmospheric circulation patterns and human activities, the potential causes of the non-stationarity of the relationship between NDVI and P/T were revealed. Results indicated that (1) the copula-based framework introduced in this study is more reasonable and reliable than the traditional double-mass curves method in detecting change points of vegetation and climate relationships; (2) generally, no significant change points were identified during 1982–2010 at the 95% confidence level, implying the overall stationary relationship still exists, while the relationships between spring NDVI and P/T, autumn NDVI and P have slightly changed; (3) teleconnection factors (including Arctic Oscillation (AO), Pacific Decadal Oscillation (PDO), Niño 3.4, and sunspots) have a more significant influence on the relationship between seasonal NDVI and P/T than local climatic factors (including potential evapotranspiration and soil moisture); (4) negative human activities (expansion of farmland and urban areas) and positive human activities (“Grain For Green” program) were also potential factors affecting the relationship between NDVI and P/T. This study provides a new and reliable insight into detecting the non-stationarity of the relationship between NDVI and P/T, which will be beneficial for further revealing the connection between the atmosphere and ecosystems.