  We study the implications of the premise that any new, relativistic, highly
energetic neutral particle that interacts with quarks and gluons would create
cascade-like events in the IceCube (IC) detector. Such events would be
observationally indistinguishable from neutral current deep-inelastic
scattering events due to neutrinos. Consequently, one reason for deviations,
breaks or excesses in the expected astrophysical power-law neutrino spectrum
could be the flux of such a particle. Motivated by features in the recent
1347-day IceCube high energy starting event data (HESE), we focus on particular
boosted dark matter ($\chi$) related realizations of this premise. Here, $\chi$
is assumed to be much lighter than, and the result of, the slow decay of a
massive scalar ($\phi$) which constitutes a major fraction of the Universe's
dark matter. We show that this hypothesis, coupled with a standard power-law
astrophysical neutrino flux is capable of providing very good fits to the
present data, along with a possible explanation of other features in the HESE
sample. These features include a) the paucity of events beyond $\sim 2$ PeV b)
a spectral feature resembling a dip or a spectral change in the 400 TeV--1 PeV
region and c) an excess in the $50-100$ TeV region. We consider two different
boosted DM scenarios, and determine the allowed mass ranges and couplings for
four different types of mediators (scalar, pseudoscalar, vector and
axial-vector) which could connect the standard and dark sectors. We consider
constraints from gamma-ray observations and collider searches. We find that the
gamma-ray observations provide the most restrictive constraints, disfavouring
the $1\sigma$ allowed parameter space from IC fits, while still being
consistent with the $3\sigma$ allowed region. We also test our proposal and its
implications against IC's recent six-year through-going muon track data.
