War Powers Against Non-State Actors Act of 2014 - Amends the War Powers Resolution to declare that the authority to use U.S. Armed Forces against non-state actors would terminate 60 days after submission of a specified presidential report explaining that use, unless: (1) the President's actions are based on a law providing for the use of military force against a non-state actor; or (2) the President notifies Congress that continued use of military force is necessary because the non-state actor poses a continuing and imminent threat to the United States or U.S. persons, and Congress does not enact a joint resolution of disapproval under expedited procedures.