In my head I always assumed they dropped it around his neck and used that as an excuse to 'oops' hang him, then Mat picks up the medallion afterwards, and its weird that jerking someone's shirt open would snap a cord. On reflection I almost wonder if RJ kinda slipped there, maybe forgot Rand couldn't Heal and kinda ham-fisted in removing the medallion so it wouldn't interfere with the attempt. Who knows? Plot-wise there's no reason to break the cord, I don't think anyone channels at Mat till after it mentions him having it around his neck again some days later, when they get out of Rhuidean Rand makes a stink demanding they Heal Mat, Moraines still gone and they don't know how to Heal, so the whole time after Rand removes the medallion till it says Mat has it back on nobody evens tries to direct the OP at him. There's really no reason to have broken the cord, but it seems to me RJ was clearly going out of his way to remove it.