The limited throughput of a digital image correlation (DIC) system hampers measuring deformations at both high spatial resolution and high temporal resolution. To address this dilemma, in this paper we propose to integrate snapshot compressive imaging (SCI)-a recently proposed computational imaging approach-into DIC for high-speed, high-resolution deformation measurement. Specifically, an SCI-DIC system is established to encode a sequence of fast changing speckle patterns into a snapshot and a high-accuracy speckle decompress SCI (Sp-DeSCI) algorithm is proposed for computational reconstruction of the speckle sequence. To adapt SCI reconstruction to the unique characteristics of speckle patterns, we propose three techniques under SCI reconstruction framework to secure high-precision reconstruction, including the normalized sum squared difference criterion, speckle-adaptive patch search strategy, and adaptive group aggregation. For efficacy validation of the proposed Sp-DeSCI, we conducted extensive simulated experiments and a four-point bending SCI-DIC experiment on real data. Both simulation and real experiments verify that the Sp-DeSCI successfully removes the deviations of reconstructed speckles in DeSCI and provides the highest displacement accuracy among existing algorithms. The SCI-DIC system together with the Sp-DeSCI algorithm can offer temporally super-resolved deformation measurement at full spatial resolution, and can potentially replace conventional high-speed DIC in real measurements.