  Close encounters between neutron stars and main-sequence stars occur in
globular clusters and may lead to various outcomes. Here we study encounters
resulting in tidal disruption of the star. Using $N$-body models, we predict
the typical stellar masses in these disruptions and the dependence of the event
rate on host cluster properties. We find that tidal disruption events occur
most frequently in core-collapsed globular clusters and that roughly $25\%$ of
the disrupted stars are merger products (i.e., blue straggler stars). Using
hydrodynamic simulations, we model the tidal disruptions themselves (over
timescales of days) to determine the mass bound to the neutron star and the
properties of the accretion disks formed. In general, we find that roughly
$80-90\%$ of the initial stellar mass becomes bound to the neutron star
following disruption. Additionally, we find that neutron stars receive
impulsive kicks of up to about $20\,$km/s as a result of the asymmetry of
unbound ejecta; these kicks place these neutron stars on elongated orbits
within their host cluster, with apocenter distances well outside the cluster
core. Finally, we model the evolution of the (hypercritical) accretion disks on
longer timescales (days to years after disruption) to estimate the accretion
rate onto the neutron stars and accompanying spin-up. As long as $\gtrsim1\%$
of the bound mass accretes onto the neutron star, millisecond spin periods can
be attained. We argue the growing numbers of isolated millisecond pulsars
observed in globular clusters may have formed, at least in part, through this
mechanism. In the case of significant mass growth, some of these neutron stars
may collapse to form low-mass ($\lesssim3\,M_{\odot}$) black holes.
