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Abstract A significant interest has emerged recently in assessing whether collimated and ultrarelativistic outflows can be produced by a long-lived remnant from a binary neutron star (BNS) merger, with different approaches leading to different outcomes. To clarify some of the aspect of this process, we report the results of long-term (i.e., ∼110 ms) state-of-the-art general relativistic magnetohydrodynamics simulations of the inspiral and merger of a BNS system of magnetized stars. We find that after ∼50 ms from the merger anα–Ω dynamo driven by the magnetorotational instability sets in in the densest regions of the disk and leads to the breakout of the magnetic field lines from the accretion disk around the remnant. The breakout is responsible for generating a collimated, magnetically driven outflow with only mildly relativistic velocities and for a violent eruption of electromagnetic energy. We provide evidence that this outflow is partly collimated via a Blandford–Payne mechanism. Finally, by including or not the radiative transport via neutrinos, we determine the role they play in the launching of the collimated wind. In this way, we conclude that the mechanism of magnetic field breakout we observe is robust and takes place even without neutrinos. Contrary to previous expectations, the inclusion of neutrino absorption and emission leads to a smaller baryon pollution in polar regions and hence accelerates the occurrence of the breakout, yielding a larger electromagnetic luminosity. Given the mildly relativistic nature of these disk-driven breakout outflows, it is difficult to consider them responsible for the jet phenomenology observed in short gamma-ray bursts.