Does he use the magic on the knife to kill? That is to say, did he use the fire blast while slicing the guy with the blade? If yes, its a violation. If no, its not a violation. It seems clear to me, but I've seen this question or variation a lot, so there must be some point that there is tension over. Is magic being used to kill a human with? is the basic question that needs to be answered in first law questions.
Components:
1.) Is a human going to die from the action you are taking?
2.) Is the action that causes their death magic, in any way or form?
The only part that would require interpretation is a 3rd point, intent, which can be handled differently from group to group, but it essentially come down to
3.) Did your use of magic have deadly intent?
If you say yes to those three points, its a violation. If you say no to one of the first two, and sometimes the third, its not a violation.