Miles Kane is a big wrestling fan; he titled this song after WWE wrestler Finn Bálor's finishing move: A diving double foot stomp off the top rope, it is known as the Coup de Grâce. Speaking on Episode 6 of music show Red Stripe presents: This Feeling TV Kane said:

"I'm a big fan of his [Finn Bálor], he's a big fan of ours. We've become mates. He was texting me so I just jokingly said Coup de Grace over this tune and it just stuck."

The song is also the title track of Miles Kane's third solo album. The singer explained to HMV.com that at first he didn't know what Bálor's Coup de Grâce was. When he found out it was the final blow, "It felt very dramatic and it felt good for the album. Then it stayed for the album, it just felt right, it's putting all my emotions for these songs to bed."

Kane wrote the song with Zach Dawes and Tyler Parkford of the band Mini Mansions. The American band were the support act during The Arctic Monkey's 2014 US headlining shows and are close to their frontman and Kane's Last Shadow Puppets partner, Alex Turner. The fourth songwriter is Loren Humphrey, the drummer of the American three piece rock band Guards.