Former X Factor contestant and mental health advocate Katie Waissel described the video as “triggering, insensitive and frankly reckless to push out as ‘entertainment'”.
“This opening visual of feet suspended above the ground is not a harmless ‘play on words’,” she wrote, adding: “The suicide imagery is impossible to ignore.”
Other social media users called the clip “insensitive”, “triggering” and in “poor taste”.
Ant and Dec said in a statement on Saturday that they had “taken on board comments” and deleted the video.
The podcast will see the duo catch up about their lives as well as taking questions and comments from listeners.
It is part of their new Belta Box brand, which will be on platforms including YouTube, Facebook, Instagram and TikTok, and will also host classic clips from their TV careers as well as “new digital formats”.
If you have been affected by any of the issues raised in this story, information and support can be found at the BBC’s Action Line.