Multi-track synthetic aperture radar interferometry (InSAR) provides a good approach for the monitoring of long-term multi-dimensional earthquake deformation, including pre-, co-, and post-seismic data. However, the removal of atmospheric errors in both single- and multi-track InSAR data presents significant challenges. In this paper, a method of spatio-temporal correlation analysis using independent component analysis (ICA) is proposed, which can extract multi-track deformation components for the accurate retrieval of earthquake deformation time series. Sentinel-1 data covering the double earthquakes in Turkey and Syria in 2023 are used to demonstrate the effectiveness of the proposed method. The results show that co-seismic displacement in the east–west and up–down directions ranged from −114.7 cm to 82.8 cm and from −87.0 cm to 63.9 cm, respectively. Additionally, the deformation rates during the monitoring period ranged from −137.9 cm/year to 123.3 cm/year in the east–west direction and from −51.8 cm/year to 45.7 cm/year in the up–down direction. A comparative validation experiment was conducted using three GPS stations. Compared with the results of the original MSBAS method, the proposed method provides results that are smoother and closer to those of the GPS data, and the average optimization efficiency is 43.08% higher. The experiments demonstrated that the proposed method could provide accurate two-dimensional deformation time series for studying the pre-, co-, and post-earthquake events of the 2023 Turkey–Syria Earthquakes.