We'd recommend archiving. This way they will not be visible on the board anymore however you can still refer back to them via the "Archived Items" section in the board.
You can also archive all cards in a list by clicking (...) in your "Done" list and select "Archive all cards in this list".
More information about archiving is available here: http://help.trello.com/article/795-archiving-and-deleting-cards
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