Building on some ideas
@donoghu mentioned, here's a theory:
The knives have magnetized tips and fly with a very powerful electromagnet positioned behind the target. Then arena, for instance, could have an electromagnet behind each wall allowing the knives to be aimed anywhere within the arena, as well as potentially changing the path midflight. String is used to make the knives initially float, but once the electromagnet is turned on, the knives move fast enough to break the string and leave them clean for examination.
Makito's epiphany from the stigmata was that the devil's marks they've been making were made from sheet copper (ch 10), which is a common material in modern electromagnets. Liese's stigmata may have been caused from some sort of copper exposure or allergy (?).