Unmuzzle the Drug Czar Act of 2014 - Amends the Office of National Drug Control Policy Reauthorization Act of 1998 to repeal a provision requiring the Director of National Drug Control Policy to: (1) ensure that no federal funds appropriated to the Office of National Drug Control Policy are expended for any study or contract relating to the legalization (for a medical or any other use) of a substance listed in schedule I of the Controlled Substances Act (which includes marijuana), and (2) oppose any attempt to legalize the use of any such substance that the Food and Drug Administration (FDA) has not approved for use for medical purposes.