Killing the first one probably won't any more than killing a single mouse doesn't stop an infestation, but once the mice realize that you got a couple of cats they will find the exit.
That's why you need to put traps by the exit too, the mice know too much and might potentially regroup to return with better tactics. You've got to get them all in one swift purge.
They didn't tell us the age of the assailant last time or the victim. I'm guessing they tend to choose words for the headline that might have the most impact.
"White Swiss man wielding a machete attacks other Swiss people and injures possibly white Swiss baby" Just doesn't seem to really fit in a headline.