Abstract We present the first relativistic magnetohydrodynamics numerical simulation of a magnetic jet that propagates through and emerges from the dynamical ejecta of a binary neutron star merger. Generated by the magnetized rotation of the merger remnant, the jet propagates through the ejecta and produces an energetic cocoon that expands at mildly relativistic velocities and breaks out of the ejecta. We show that if the ejecta has a low-mass (∼10−7 M⊙) high-velocity (v ∼ 0.85c) tail, the cocoon shock breakout will generate γ-ray emission that is comparable to the observed short GRB170817A that accompanied the recent gravitational wave event GW170817. Thus, we propose that this gamma-ray burst (GRB), which is quite different from all other short GRBs observed before, was produced by a different mechanism. We expect, however, that such events are numerous and many will be detected in coming LIGO–Virgo runs.