  We explore the possibility that high-energy (HE) neutrinos produced from
choked jets can be annihilated with low-energy (LE) neutrinos emitted from the
accretion disk around a black hole in binary neutron star mergers and rare
core-collapse supernovae. For HE neutrinos produced close to the stellar center
($\lesssim 10^{9}-10^{12}$ cm), we find that the emerging all-flavor spectrum
for neutrinos of $E\gtrsim 0.1-1$ PeV could be modified by a factor $E^{-n}$
with $n\gtrsim 0.4-0.5$ under realistic conditions. Flavor evolution of LE
neutrinos does not affect this result but can change the emerging flavor
composition of HE neutrinos. As a consequence, the above annihilation effect
may need to be considered for HE neutrinos produced from choked jets at small
radii. We briefly discuss the annihilation effects for different HE neutrino
production models and point out that such effects could be tested through
precise measurements of the diffuse neutrino spectrum and flavor composition.
