Seconds-long numerical-relativity simulations for black hole-neutron star mergers are performed for the first time to obtain a self-consistent picture of the merger and post-merger evolution processes. To investigate the case that tidal disruption takes place, we choose the initial mass of the black hole to be $5.4M_{\odot }$ or $8.1M_{\odot }$ with the dimensionless spin of 0.75. The neutron-star mass is fixed to be $1.35M_{\odot }$. We find that after the tidal disruption, dynamical mass ejection takes place spending $\lesssim 10\mathrm{ms}$ together with the formation of a massive accretion disk. Subsequently, the magnetic field in the disk is amplified by the magnetic winding and magnetorotational instability, establishing a turbulent state and inducing the angular momentum transport. The post-merger mass ejection by the magnetically-induced viscous effect sets in at $\sim 300$-$500\mathrm{ms}$ after the tidal disruption, at which the neutrino luminosity drops below $\sim 10^{51.5}erg/s$, and continues for several hundreds ms. A magnetosphere near the rotational axis of the black hole is developed after the matter and magnetic flux fall into the black hole from the accretion disk, and high-intensity Poynting flux generation sets in at a few hundreds ms after the tidal disruption. The intensity of the Poynting flux becomes low after the significant post-merger mass ejection, because the opening angle of the magnetosphere increases. The lifetime for the stage with the strong Poynting flux is $1$-$2\mathrm{s}$, which agrees with the typical duration of short-hard gamma-ray bursts.