In the dicitionary, one definition of Serious, under serious problems, is- Life and death. To take life- is to kill. So the whole clue makes sense when you break it down.
John McEnroe wrote a book called "Serious"- very good actually. Loved watching him as a kid. He used to say, rather a lot, during many a tennis match, " You cannot be serious" to the umpires with looks that could kill, too;-)