Just to add to the dialectical data points, my North Carolina-born dad and his siblings “cut off” lights, stoves, and televisions.
“Crop Dusting” is another variant, specifically referring to when someone is just walking by and gone by the time the … dust … settles.
Let’s not forget the slang ‘turd cutter’, as in she has a nice turd cutter. While it typically refers to the cheeks the actual turd cutter is the anus, & if it’s already cutting one thing coming out of it it’s not a far leap to have it cutting off air coming out of it.
I think “cut and run” refers to sailors cutting the ship’s mooring lines (instead of unlashing them) to make a quick getaway from port.