The pair were recruited from the music industry when Gum was launched in September 2005 to bring in a greater understanding of popular culture to the youth-focused arm.
After joining, they were given a future equity stake in the business, to accrue once it started making money. It is understood that this will now revert back to Saatchi & Saatchi.
Neumann and Amos will continue to work on projects with Gum while they set up their as yet un-named venture, which will be backed by hedge-fund investment.
Their exit comes at the same time as several job losses at Saatchi & Saatchi.
A spokeswoman said: "We are consulting with a limited number of individuals on their roles. Regrettably, this is likely to result in redundancies."