With the observation of high-energy astrophysical neutrinos by the IceCube Neutrino Observatory, interest has risen in models of PeV-mass decaying dark matter particles to explain the observed flux. We present two dedicated experimental analyses to test this hypothesis. One analysis uses six years of IceCube data focusing on muon neutrino track events from the Northern Hemisphere, while the second analysis uses two years of cascade events from the full sky. Known background components and the hypothetical flux from unstable dark matter are fitted to the experimental data. Since no significant excess is observed in either analysis, lower limits on the lifetime of dark matter particles are derived: We obtain the strongest constraint to date, excluding lifetimes shorter than $10^{28},$s at $90%$ CL for dark matter masses above $10,$TeV.