Young pulsars apparently have a distribution of initial power outputs N (> Po−γ), with 1/2 < γ < 1 and Po ≳ 1038 ergs/sec. Assuming that ultra-high-energy (E ≳ 1015 eV) cosmic-ray nuclei are accelerated at the central pulsar, a young, dense supernova shell can be a powerful source of high-energy neutrinos. With an optical array placed in a volume of one km3 at great ocean depths, as proposed for the DUMAND detector, it is likely that ≳ 103 hadronic and electromagnetic cascades induced by neutrinos would be recorded for a stellar collapse within our Galaxy. Such supernovae occur about 8 times per century. Neutrinos from young supernova shells in the Virgo supercluster would be marginally detectable via neutrinos with N(> Po) ∝ Po−1/2, but unobservable if N(> Po) ∝ Po−1.