Havahart makes live traps in larger sizes. I've used the smaller one to trap attic squirrels. Once you've caught it you can drown it, shoot it, relocate it, whatever. The slingshot might only result in an injured animal, not a kill.
Oh, he’s too wily for the trap? Try a different bait...peanut butter works on most other rodents.
Right...I didn’t have one big enough to get a woodchuck. I have tried all kinds of things to drive it off, even borrowed a trap and got a skunk instead which was a real pain.
I hit the woodchuck square on the butt, but I think they have so much blubber, it didn’t even twitch. (Using 3/8” ball bearing)