expression, godan verb (-ru)
interrupt; butt in; cut someone off
Idiomatic expression for breaking the flow of a conversation, often by changing the subject or interjecting at an awkward moment. The image is of 'breaking the back' of the talk.
彼が話しているときに、話の腰を折らないでください。
Please don't interrupt him while he's talking.
I was having an important conversation, but she cut me off.