Note the pronunciation is zhòng (4th tone), not zhōng (1st tone). Here 中 means 'to hit the mark' - the slander hits and wounds. This is the same 中 as in 中毒 (to be poisoned).
usage
Stronger and more literary than 说坏话 (to say bad things about). 中伤 implies deliberate, targeted defamation that causes real reputational damage.
