"To delete" is to "deletion" as "to discard" is to what?
The thing that is deleted is a deletion; the thing that is discarded is a discard.
The act of deleting is a deletion; the act of discarding is a discarding.
If you like using incredibly rare words, you can use discardure for the act of discarding, as Jon Hanna's answer says. Expect people to think it's not a real word.
Discardure, though it is not a common word, used primarily in legal contexts.