The future fusion reactor devices built by Institute of Plasma Physics, Chinese Academy of Science (ASIPP) will be a compact burning plasma facility to fill the gap between ITER and the China Fusion Engineering Test Reactor (CFETR), with the mission of studying the Deuterium-Tritium (D-T) plasma in steady-state operation. The winding-package (WP) of its toroidal field coil (TFC) is graded into high-field WP and low-field WP, and the high critical current density (Jc) Nb3Sn strand will be applied to the high-field WP based on the current design. The thermo-magnetic instability is the main issue in the application of high-Jc Nb3Sn strand, which may induce premature quenching in the low field regions. This issue can be improved by reducing the effective filament diameter to suppress flux jumps and increasing the residual resistivity ratio (RRR) to enhance the release of heat generated by flux jumps. However, in the conductor manufacturing process, local plastic deformations of strands can impact the sub-element layout and degrade the RRR of the strand, which would increase again the risk on instability. In this study, magnetization measurements and V-I tests were performed on samples with different indentation depths. The hysteresis loss and deff of the indented sample was obtained from the test results. The impact of local plastic deformation on the thermo-magnetic instability of two types of Nb3Sn strand was confirmed by cross-sectional metallographic observation and quantitative microstructure analysis. It was shown that flux jumps were suppressed at indentation depths below 0.3 mm. Further indentation increase leads to severe flux jumps.