Yes, technically being a kids' show, at least from what I saw and have read in the comics. They certainly *tried* to kill, tho, both Bat-team members and regular civilians. (And I'm pretty sure in the ep Two of a Kind, Joker killed some squirrels. Poor, poor squirrels.)
However, this Joker did do some very dastardly things (frex torturing cop Ethan Bennett and turning him into Clayface, also bringing Harley into the villain fold)