The Spider-killing Curse is a spell used to kill or, at least, blast back Acromantulas or other large spider species.
Harry uses this in the Forbidden Forest against the attacking Acromantulas in the film version of Harry Potter and the Chamber of Secrets. He learned this from Tom Marvolo Riddle, who attempted to use it against Aragog in the memory Harry visits.
 Possible Etymology
From the Latin aranea, meaning “spider”, and exuo, meaning “I lay aside”.