Recent weak lensing surveys have revealed that the direct measurement of the parameter combination $S_8equivsigma_8(Omega_m/0.3)^{0.5}$ -- measuring the amplitude of matter fluctuations on 8 $h^{-1}$Mpc scales -- is $sim3sigma$ discrepant with the value reconstructed from cosmic microwave background (CMB) data assuming the $Lambda$CDM model. In this Letter, we show that it is possible to resolve the tension if dark matter (DM) decays with a lifetime of $text{log}_{10}(Gamma^{-1}/ text{Gyr})= 1.75_{-0.95}^{+1.4}$ into one massless and one massive product, and transfers a fraction $varepsilonsimeq 0.7^{+2.7}_{-0.6}%$ of its rest mass energy to the massless component. The velocity-kick received by the massive daughter leads to a suppression of gravitational clustering below its free-streaming length, thereby reducing the $sigma_8$ value as compared to that inferred from the standard $Lambda$CDM model, in a similar fashion to massive neutrino and standard warm DM. Contrarily to the latter scenarios, the time-dependence of the power suppression and the free-streaming scale allows the 2-body decaying DM scenario to accommodate CMB, baryon acoustic oscillation, growth factor and uncalibrated supernova Ia data. We briefly discuss implications for DM model building, galactic small-scale structure problems and the recent Xenon-1T excess. Future experiments measuring the growth factor to high accuracy at $0lesssim zlesssim1$ can further test this scenario.
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