they were killed by the hand of David and by the hand of his servants

Here "by the hand of" means "through" or "by." This can be stated in active form. Alternate translation: "David and his servants killed them" (See: rc://en/ta/man/jit/figs-idiom and rc://en/ta/man/jit/figs-activepassive)

his servants

"his soldiers." These men served David as soldiers. See how you translated this phrase in 2 Samuel 3:22.