(Sorry about inserting the comment about the "wee pen knife". It's a red herring I think. This weapon has it's own thread with much discussion about it. It's just that we haven't found a reference to one along with mention of straw.)

Thank you for the other comments, all.
I do favour Don's suggestion as making the most sense - inasmuch as you can make sense of ballad-speak.
It's an image I'll rather like to call up when I sing or hear these songs from now on. It always appears at a point of high drama.

Q, True-Love tells a story about taking his knife to a knife-sharpener in an Eastern European city, back in the 60s. The fearsome-looking expert did the knife-cuts-straw trick with a great flourish before handing it back. It's a powerful image.
                            Cheers, Joy