We propose heavy decaying dark matter (DM) as a new probe of the cosmic neutrino background (C
νB). Heavy DM, with mass
≳109 GeV, decaying into neutrinos can be a new source of ultra-high-energy (UHE) neutrinos. Including this contribution along with the measured astrophysical and predicted cosmogenic neutrino fluxes, we study the scattering of UHE neutrinos with the C
νB via standard weak interactions mediated by the
Z-boson. We solve the complete neutrino transport equation, taking into account both absorption and reinjection effects, to calculate the expected spectrum of UHE neutrino flux at future neutrino telescopes, such as IceCube-Gen2 Radio. We argue that such observations can be used to probe the C
νB properties, and in particular, local C
νB clustering. We find that, depending on the absolute neutrino mass and the DM mass and lifetime, a local C
νB overdensity
≳106 can be probed at IceCube-Gen2 Radio within 10 years of data taking.