Earthquake rupture speeds exceeding the shear-wave velocity have been reported for several shallow strike-slip events. Whether supershear rupture also can occur in deep earthquakes is unclear, because of their enigmatic faulting mechanism. Using empirical Green's functions in both regional and teleseismic waveforms, we observed supershear rupture during the 2013 moment magnitude (M-w) 6.7 deep earthquake beneath the Sea of Okhotsk, an aftershock of the large deep earthquake (M-w 8.3). The M-w 6.7 event ruptured downward along a steeply dipping fault plane at an average speed of 8 kilometers per second, suggesting efficient seismic energy generation. Comparing it to the highly dissipative 1994 M-w 8.3 Bolivia earthquake, the two events represent end members of deep earthquakes in terms of energy partitioning and imply that there is more than one rupture mechanism for deep earthquakes.