We present Keck/DEIMOS spectroscopy of globular clusters (GCs) around the ultra-diffuse galaxies (UDGs) VLSB−B, VLSB−D, and VCC615 located in the central regions of the Virgo cluster. We spectroscopically identify 4, 12, and 7 GC satellites of these UDGs, respectively. We find that the three UDGs have systemic velocities (V sys) consistent with being in the Virgo cluster, and that they span a wide range of velocity dispersions, from ∼16 to ∼47 km s−1, and high dynamical mass-to-light ratios within the radius that contains half the number of GCs (, , , respectively). VLSB−D shows possible evidence for rotation along the stellar major axis and its V sys is consistent with that of the massive galaxy M84 and the center of the Virgo cluster itself. These findings, in addition to having a dynamically and spatially (∼1 kpc) off-centered nucleus and being extremely elongated, suggest that VLSB−D could be tidally perturbed. On the contrary, VLSB−B and VCC615 show no signs of tidal deformation. Whereas the dynamics of VLSB−D suggest that it has a less massive dark matter halo than expected for its stellar mass, VLSB−B and VCC615 are consistent with a ∼1012 M ⊙ dark matter halo. Although our samples of galaxies and GCs are small, these results suggest that UDGs may be a diverse population, with their low surface brightnesses being the result of very early formation, tidal disruption, or a combination of the two.