The ZEPLIN-III experiment is operating in its second phase at the Boulby Underground Laboratory in search of dark matter WIMPs. The major upgrades to the instrument over its first science run include lower background photomultiplier tubes and installation of a plastic scintillator veto system. Performance results from the veto detector using calibration and science data in its first six months of operation in coincidence with ZEPLIN-III are presented. With fully automated operation and calibration, the veto system has maintained high stability and achieves near unity live time relative to ZEPLIN-III. Calibrations with a neutron source demonstrate a rejection of 60% of neutron-induced nuclear recoils in ZEPLIN-III that might otherwise be misidentified as WIMPs. This tagging efficiency reduces the expected untagged nuclear recoil background from neutrons during science data taking to a very low rate of ~0.2 events per year in the WIMP acceptance region. Additionally, the veto detector provides rejection of 28% of gamma-ray induced background events, allowing the sampling of the dominant source of background in ZEPLIN-III - multiple scatter gamma-rays with rare topologies. Since WIMPs will not be tagged by the veto detector, and tags due to gamma-rays and neutrons are separable, this population of multiple scatter events may be characterised without biasing the analysis of candidate WIMP signals in the data.