  The decay of asymmetric dark matter (ADM) can lead to distinct neutrino
signatures characterized by an asymmetry between neutrinos and antineutrinos.
In the high-energy regime, the Glashow resonant interaction $\bar{\nu}_{e} +
e^{-} \rightarrow W^{-}$ yields an increase in sensitivity to the neutrino
flux, and stands out as the only way of discerning the antineutrino component
in the diffuse high-energy astrophysical neutrino flux. This offers a unique
opportunity in the search for dark matter with masses above the PeV scale. We
examine the neutrino signal stemming from ADM decay and set the first stringent
constraints on ADM lifetime $\tau_X$. For ADM with mass $m_X\gtrsim 10$ PeV, we
find $\tau_X\lesssim 10^{29}$s using the data from the recent IceCube search
for Glashow resonance events. Our projections further show that sensitivities
at the forthcoming IceCube-Gen2 could approach $10^{30}$s, depending on the
decay channel. The current constraints on symmetric dark matter decay to
neutrinos are also improved by up to a factor of 3 thanks to the Glashow
resonance.
