The song was originally supposed to be released as a single and a music video was filmed by the director Tim Broad, and opens with a picture of the poet Oscar Wilde hanging on a brick wall, and features scenes of the group-iconic Salford Lads Club and surrounding areas being bicycled through by the lads and friends. Because of a reference to "plan a mass murder" in one lyric it was banned from daytime airplay by the BBC because of the then recent Hungerford massacre, so the band decided not to release it in the UK, however it was released in various other regions including North America, Europe, Australia and Japan.

"Stop Me If You Think You've Heard This One Before" was subsequently included on the compilation album Stop Me and on The Very Best of The Smiths. The song is also included in the music game Rock Band 3.

The cover of the single is a picture of British actor and singer Murray Head from a film still of the 1966 film The Family Way (a movie that would also be the source of the photograph on the cover of I Started Something I Couldn't Finish). There are four different versions of the cover, each tinted a different colour (red, orange, blue and grey) depending on the region.

In 2007, the song was re-composed as "Stop Me" with additional lyrics from the song "You Keep Me Hangin' On" by The Supremes by British DJ Mark Ronson featuring Daniel Merriweather on the vocals. Merriweather admitted in an interview with The Guardian that he was not very familiar with the original before he recorded Mark Ronson's revised version. He explained: "Mark said, 'I want you to sing on this – it's my favourite Smiths song,' so I listened to it. I'd heard it once before, but I was never a Smiths fan. But I thought it was beautiful." The song was later released as a single on 2 April 2007 on Columbia Records with the shortened name "Stop Me", and featured on the compilation album Version. The music video, released at the same time as the song, features a man who finds a pair of trainers that control him and force him to run along the motorway near the Blackwall Tunnel. This version was released in the United Kingdom. The international version showed people crying animated tears. Live versions by Mark Ronson and/or Stu Zender featuring Merriweather have appeared on Conan O'Brien (on July 2007), BBC Radio 1 and Jimmy Kimmel Live!).

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