Stop Corporate Inversions Act of 2014 - Amends the Internal Revenue Code to revise rules for the taxation of inverted corporations (i.e., U.S. corporations that acquire foreign companies to reincorporate in a foreign jurisdiction with income tax rates lower than the United States) to provide that a foreign corporation that acquires the properties of a U.S. corporation or partnership after May 8, 2014, shall be treated as an inverted corporation and thus subject to U.S. taxation if, after such acquisition: (1) it holds more than 50% of the stock of the new entity (expanded affiliated group), or (2) the management or control of the new entity occurs primarily within the United States and the new entity has significant domestic business activities.