  We study the cutoff for the cosmic-ray neutrino, set by the scattering with
cosmic background neutrinos into dark sector particles through a neutrino
portal interaction. We find that a large interaction rate is still viable, when
the dark sector particles are mainly coupled to the $\tau-$neutrino, so that
the neutrino mean free path can be reduced to be $O(10)~$Mpc over a wide energy
range. If stable enough, the dark sector particle, into which most of the
cosmic-ray neutrino energy is transferred, can travel across the Universe and
reach the earth. The dark sector particle can carry the energy as large as
$\O({\rm EeV})$ if originates from a cosmogenic neutrino.
