The proliferation of phasor measurement units (PMUs) presents new challenges in archiving and processing large amounts of synchrophasor data which necessitates advanced data compression methods. This paper proposes a singular value decomposition (SVD)-based method for compression of synchrophasor data, including magnitude, phase-angle, and complex phasor. The proposed method includes a dimensionality evaluation and reduction technique and a real-time progressive partitioning algorithm. The proposed dimensionality reduction technique employs the measurement uncertainty of PMUs and introduces a threshold criterion on the signal-to-noise ratio (SNR) of SVD modes. Singular modes with high SNR are retained, and those dominated by measurement error are discarded to achieve a high compression ratio (CR) while preserving the critical information with adequate accuracy. The proposed progressive partitioning separates the data corresponding to normal and disturbance conditions by monitoring the dimensionality variations in real-time. The partitions containing the data of similar dimensionality are separately compressed to further improve the accuracy and CR. The performance of the proposed method is evaluated and benchmarked against state-of-the-art methods using both field and simulated PMU data. The results show that the proposed method provides high CR while accurately preserving the critical information of events and disturbances.