Two-dimensional disordered superconductors with broken spin-rotation and time-reversal invariance, e.g., with px+ipy pairing, can exhibit plateaus in the thermal Hall coefficient (the thermal quantum Hall effect). Our numerical simulations show that the Hall insulating regions of the phase diagram can support a sub-phase where the quasiparticle density of states is divergent at zero energy, ρ(E)∼∣E∣∣1∕z−1, with a nonuniversal exponent z>1, due to the effects of rare configurations of disorder (Griffiths phase).