Both boys were discharged from hospital by yesterday afternoon, and school headmaster Steve Cole said he understood they were doing well.
However, he admitted the school was still in the dark as to how the incident could have occurred, saying the antique blade had been made safe.
The prop was a razor that had been blunted and wrapped in several protective layers, Mr Cole said.
"It's normal for Sweeney Todd to have such an instrument [and it] clearly had been checked many, many times," he said.
"It has been bound and cellophaned and all sorts of things. It had been blunted and had been through all sorts of health and safety checks. It was a very unfortunate mistake."
The scene had been performed "many times" since January, including eight dress rehearsals where the prop was used.
When asked how two boys ended up with the sides of their necks cut Mr Cole last night said he didn't know.
"I've got no idea. I've got no idea."
The unfortunate incident happened halfway through the second act, Mr Cole said.
The performance continued and audience members were unaware of the incident.
The school put the production run on hold last night but Mr Cole said he hoped the Friday, Saturday and Sunday shows would go ahead but "without those particular props".
Senior staff at the school spent much of yesterday in crisis meetings, and a police investigation is under way.
"It's not a criminal inquiry. In this instance the play is not the reality," said a police spokesman.
WorkSafe New Zealand is also looking into the incident, but Mr Cole said he was not concerned about possible consequences for the school under new health and safety laws which came into force on Monday.
"We're very confident in our health and safety procedures.
"My concern is for the two boys and their families."
The owner of an antique shop where the razors were bought said the person who purchased them had talked to one of his staff members about the need to cover up the sharp edge.
The man, who asked the Herald not to name him, could not immediately recall whether the man had mentioned it would be a high school production.
"I know they discussed the safety element and maybe covering up the blade."
Sweeney Todd is about an English barber and serial killer who kills his customers with a razor and, with the help of struggling pie shop owner Mrs Lovett, turns their corpses into meat pies.
In 2007 the musical was made into a film starring Johnny Depp and Helena Bonham Carter.