In 2012 Mulligan was sentenced to three months' home detention for assaulting his sister.
Last week it emerged that 18 prisoners were currently without their electronic bracelets, after a report that five criminals serving community-based sentences or on electronic monitoring were on the run after cutting off their ankle bracelets.
Prime Minister John Key admitted he was "a little bit surprised" to learn how many prisoners had "slipped" their electronic monitoring bracelets and were on the loose.
Corrections assistant northern commissioner Alastair Riach said alarms were raised immediately if bracelets were cut.
"We know who they are. Police will be prioritising, depending on the risk, the effort they will put into locating these people."
Convicted child-sex offender David Livingstone was caught this month after he cut off his bracelet.
Last year Tony Robertson murdered and raped North Shore woman Blessie Gotingco while on monitored release for child-sex offending.
There are 3232 offenders on the electronic monitoring system introduced in February - 1832 are also monitored via a real-time GPS system.
Invercargill police are urging anyone with information to contact them on their Facebook or by calling (03) 211 0400.
Information can also be left anonymously through Crimestoppers on 0800 555 111. or by calling (03) 211 0400.