To engage in an activity, usually an aimless or idle one, to occupy oneself, especially with the goal of making the amount of time seem to pass more quickly or less slowly. I'm going to walk down to the bookstore to kill a couple hours before my flight. Do you want anything? The game is great if you want to kill a few minutes here and there, but it gets pretty tiresome playing it for long stretches.

To overexert oneself or overextend one's effort while doing something. Don't kill yourself trying to get the report done tonight—it's not due until next week anyway. They're killing themselves finishing the last touches on the exterior of the house before the storm hits us.