Dark matter currently makes up approximately 84% of the matter in our universe, but has yet to be observed. A recent model by Grossman, Harnik, Telem, and Zhang proposes a new form of dark matter called self-destructing matter which could decay to standard model leptons after an interaction in Earth. Motivated by this model, in this analysis we perform two distinct analyses looking at high energy events in the Sudbury Neutrino Observatory data between 1999 and 2003. In the first, we perform a null hypothesis test on the data between 20 MeV and 10 GeV to look for any data which is not consistent with atmospheric neutrinos and find no evidence for new physics. In the second analysis we perform a dedicated search for back to back lepton pairs from a slow dark mediator in the self-destructing dark matter model. We find no evidence for the self-destructing dark matter and place new limits on the rate of these events.