In this paper, a scheme of signal extraction and modeling for GNSS position time series based on Monte Carlo Multi-channel Singular Spectrum Analysis (MC-MSSA) is introduced, which can effectively consider the spatial correlation of different directions by processing the different components of position time series at the same time. Meanwhile, the Monte Carlo significance test is utilized to distinguish the signal from the colored noise. By comparing with Singular Spectrum Analysis (SSA), it can be confirmed that MSSA has better signal extraction and modeling performance by taking into account the correlation of different channels. Then, taking the LHAZ station as an example, MC-MSSA is utilized to simultaneously model the three components of GNSS position time series, and the trend and periodic signals are respectively identified by Kendall nonparametric test and W-correlation correlation analysis. The result denotes that MC-MSSA can effectively model the tectonic and non-tectonic signals of GNSS position time series, and the modeled signals can more intuitively reflect the dynamic movement of the station. Finally, based on the MC-MSSA-modeled tectonic signal, we characterize the crustal deformations around the eastern Tibetan Plateau, mainly including the crustal movement and strain rate change. The results suggest that the pushing movement of the Tibetan Plateau from the Indian plate is blocked by the South China block, and the crustal movement rate is obviously decreased and appears a right-handed movement trend. Meanwhile, the junction of the Tibetan Plateau and South China block has accumulated a certain amount of stress, and the tectonic activity at the junction is relatively strong and still belongs to the dangerous zone of seismic activity.