Entry from OED Online

[Origin uncertain. Perh. an extended use of MULLET-HEAD n. 2; but Grand Royal (1995) No. 2 proposes a number of other, largely humorous origins, including a relationship with MULLET n.¹ and with the obsolete MULLET v.
  Apparently coined, and certainly popularized, by U.S. hip-hop group the Beastie Boys (see quot. 1994), who also publish Grand Royal.] 

    A hairstyle, worn esp. by men, in which the hair is cut short at the front and sides, and left long at the back.
 
  1994 Mullet Head (song) in ‘Beastie Boys’ Tour Shot! (CD notes), You wanna know what's a mullet? well I got a little story to tell About a hair style, that's way of life Have you ever seen a Mullet wife? 1995 Grand Royal No. 2. 46 The Mullet does not discriminate, though it is rare to see one worn by a senior citizen of any stripe. 1997 Independent on Sunday 2 Feb. (Real Life section) 2/1 Connoisseurs of the absurd in gentlemen's hairdressing have been enjoying a laugh at..those unfortunates who continue to commit that most heinous fashion don'tthe Mullet. 1998 Sunday Mirror 12 Apr. (Personal suppl.) 3/2 The Mullet... If you have one, then a word in your ear: Scissors. 2000 Sunday Herald (Glasgow) 16 Apr. (Seven Days section) 1/4 A malodorous guy with a flowing mullet.