Archer found himself in the bottom two alongside Lloyd Daniels after the public vote. Both acts then had to perform a song of their choice to persuade the judges to keep them in the competition.
Archer was first to perform, and chose to sing Queen's 'The Show Must Go On'. Daniels followed with a rendition of 'Last Request' by Paolo Nutini.
After their performances, the judges had to decide who to send home. Simon Cowell was first to vote and sent home Daniels, saving his own act Archer. Meanwhile, Cheryl Cole, who mentors Daniels, sent home Archer.
Louis Walsh decided to send home Archer, claiming that Daniels has more "potential" and "appeal".
Dannii Minogue had the deciding vote, and said: "This is hard because nobody wants to send anybody home. We have two popstars in front of us. We're looking for a recording artist, with great performances.
"For me it's not about deadlock or not deadlock, it's about who sang the best. The act I'm sending home tonight is Lloyd."
As both acts had two votes each, the result went to deadlock. Host Dermot O'Leary announced that Archer had the fewest public votes and would be leaving the competition.
On hearing the decision, Archer said: "I just want to thank everyone who supported me and it's not the end, it's the beginning."
His mentor Simon Cowell added: "I'm sorry for Jamie. I let him down, probably, with the song choice. It's just one of the things. The brilliant thing is he's had a platform, millions of people know his name.
"We had a few spats but he's a great guy, a genuinely nice person, and I think he's got a great future ahead of him."
The X Factor continues next Saturday at 8pm on ITV1.