His comments come after a spate of assaults against staff at the prison have been linked to "hyper-violent" street gang the Crips.
A source told the Otago Daily Times the assaults had left staff at the prison fearing for their safety.
Mr Mitchell said staff safety was "an absolute priority for me because no assault on any staff member is acceptable".
"There is no excuse for these unprovoked and gutless assaults, and Corrections are ensuring the perpetrators are held to account."
He acknowledged staffing was a key element to staff safety, saying at present 81.4% of positions were filled at Otago Corrections Facility (OCF).
There were 243 applications for roles at the prison in June, he said.
"While the threat of violence is something we cannot eliminate entirely, I am working alongside Corrections and our unions to ensure our prisons provide the safest environment possible for staff and prisoners."
As part of National’s coalition agreement with New Zealand First, it committed to introducing the Protection for First Responders and Prison Officers Bill.
"This will create a specific offence for assaults on first responders, which includes mandatory prison sentences," he said.
He said nationally, Corrections received more than 33,500 applications for frontline roles between October 1, 2022, and April 29, 2024.
Corrections Association New Zealand vice-president Paul Dennehy said the union was aware of the number of applicants being high, but that did not always translate into actual recruitment.
"This is not a job for everyone and the New Zealand public have little or no understanding of what occurs inside the wall, and if people were honest, they prefer not to.
"Corrections Officers have a difficult, thankless, and dangerous job — [they] are the unsung heroes of the first responder community."
Mr Dennehy said while OCF was fortunate to be among one of the better-staffed prisons in New Zealand, any staffing shortage for frontline roles affected staff safety "without question".
"When a unit or site isn’t fully staffed, the daily routine and regiment cannot be safely managed without compromising staff and prisoner safety.
"Corrections staff work hard to make sure that staffing levels have minimal impact on prisoners, because we understand the effect this has. However, there are times when this will occur."
Retaining staff was also a problem facing OCF.
Mr Dennehy said the wages staff received did not address the work they did in a hostile and violent environment, and they wanted the department to recognise and value the hard work they did.
