not a teacher
In Australian and New Zealand English, both "cut in on him" and "cut him off" are used.
The second phrase is also common when the driver is prevented from going somewhere in particular.
"I wanted to change lanes for the turn-off, but a truck cut me off on the inside and I had to take the next exit".
I can't say I've heard the examples that emsrd2 gives, with this meaning. Perhaps I don't keep such racy company.