Knife YES but reading the link to the incident of the beginner kiter dying in those circumstances makes me think the real question is:

"Should an instructor have more than one student in the water with a kite at any time ? "

f&@k me, 4 students at once !!!!! A guy on Viccos south coast got put in hospital a couple of years ago in similar circumstances, 1 instructor and 4 or 5 students, one beginner kite looped onto beach. I hope Aussie instructors aren't still doing this.

And his option of putting the boat between the beginner kiter and kite !!!! WTF ?

kiteforum.com/viewtopic.php?f=1&t=2343820&start=120

These guys went into heaps of detail a few years ago - info is still relevant I guess.
They came to the following conclusions:
Full bladed knifes with serration in sheaf, or hook knife with double blades (single blade hook knives wont cut).
All the detail on the blog.