  We present the first set of numerical relativity simulations of binary
neutron mergers that include spin precession effects and are evolved with
multiple resolutions. Our simulations employ consistent initial data in general
relativity with different spin configurations and dimensionless spin magnitudes
$\sim 0.1$. They start at a gravitational-wave frequency of $\sim392$~Hz and
cover more than $1$ precession period and about 15 orbits up to merger. We
discuss the spin precession dynamics by analyzing coordinate trajectories,
quasi-local spin measurements, and energetics, by comparing spin aligned,
antialigned, and irrotational configurations. Gravitational waveforms from
different spin configuration are compared by calculating the mismatch between
pairs of waveforms in the late inspiral. We find that precession effects are
not distinguishable from nonprecessing configurations with aligned spins for
approximately face-on binaries, while the latter are distinguishable from a
nonspinning configurations. Spin precession effects are instead clearly visible
for approximately edge-on binaries.
  For the parameters considered here, precession does not significantly affect
the characteristic postmerger gravitational-wave frequencies nor the mass
ejection. Our results pave the way for the modeling of spin precession effects
in the gravitational waveform from binary neutron star events.
