Joseph could not be reached Wednesday for comment. No one answered the telephone at a number believed to be his.
In a statement to Politico, Joseph took "complete responsibility" for the Twitter feed, saying it started as a "parody account." He apologized to those he insulted.
A White House official confirmed that Joseph no longer works for the administration, but declined further comment on personnel matters.
White House spokesman Jay Carney said Wednesday he had no additional information to provide.
He said White House staffers cannot access social media sites like Twitter from the White House unless they have an official, authorized account. Carney and many other senior administration officials have official Twitter accounts and often send many tweets a day.