"The Elder Wand is simply the most ruthless of wands in that it will only take into consideration strength. So one would expect a certain amount of loyalty from one's wand. So even if you were disarmed while carrying it, even if you lost a fight while carrying it, it has developed an affinity with you that it will not give up easily. If, however, a wand is won, properly won in an adult duel, then a wand may switch allegiance... However, the Elder Wand knows no loyalty except to strength. So it's completely unsentimental. It will only go where the power is. So if you win, then you've won the wand. So you don't need to kill with it. But...almost inevitably, it attracts wizards who are prepared to kill and who will kill. And also it attracts wizards like Voldemort who confuse being prepared to murder with strength."

You don't need to kill, just take it from the owner. Just happens that most people who want it, will kill for it.