The movie star was shooting the harrowing film with eccentric director Stanley Kubrick when his pregnant wife CARI was taken to hospital, and he couldn't get permission to take a break from the project to welcome his kid into the world.
Modine says, "We had arrived at a point of madness on the set and it was really scary; and my first child was being born in an emergency Caesarian.
"I don't think that he (Kubrick) ever believed he was going to do more than three takes or five takes; that he'd work on a scene for more than one day or that a scene would turn into a week or a month.
"We were filming one scene for already a week and a half and if you challenged him on that it was the most insulting thing that you could say to him. So I told him, 'Look, I've got to go.'
"He was a very practical man, not trying to be mean or malicious, so he said, 'No. What are you gonna do? You're not a doctor. You're not gonna deliver the child? Are you gonna be there to cut the umbilical cord?'
"It just didn't make any sense to him. So I thought, 'Drastic situations are cause for drastic measures,' and that was one of those things that required a drastic measure. It wasn't something that was premeditated. It was something I found myself doing - threatening to cut my hand. It was an insane moment.
"I'm so happy that he agreed to let me go and not make me cut my hand... I didn't make him godfather, by the way."