The new service, called Menshn.com (a take on the word "mention" rather than the MP's name), launched yesterday exclusively in the US.
Mensch told reporters that the social network would aim to cut out the irrelevant chatter that she feels is a blight on microblogging site Twitter, thus allowing people to debate real subjects and topics.
The Corby MP has built up a strong media profile in part thanks to her more than 60,000 followers on Twitter, along with her role on the Commons culture, media and sport committee dissecting the aftermath of the UK phone hacking scandal.
To launch Menshn.com, she teamed up with Luke Bozier, a former aide of Tony Blair who defected to the Tories in January.
Billed as a network for "talking on topic", the site is launching in the US with the hope of attracting online debate around the forthcoming presidential election.
It is understood that the plan is to launch the service in Britain in time for the London 2012 Olympics this summer.
Menshn.com works similarly to Twitter in that members post short messages and links, but the core difference is that discussion is focused on pre-approved topics, in an attempt to restrict the spam messages that often arise from Twitter hashtags.
The MP has also previously complained of being targeted by explicit and "misogynistic" messages online after television appearances.
Speaking to The Guardian, Mensch said that she had the idea for launching Menshn.com at Christmas 2011, after being a "passionate user" of social media "since the days of AOL chatrooms".
She said that both herself and Bozier had become frustrated "at the way Twitter doesn't focus on topics".
"We both love Twitter, but if you want to focus on the election there's no obvious place to do than online. Twitter is just too random," she told the paper.
"We wanted to encourage people to have conversations rather than broadcast their thoughts."
The Guardian says that Mensch and Bozier have incorporated a private company, called MenschBozier Ltd, for the site, in which they both have a 50% stake.
But Mensch said that they would most likely look for venture capital funding in the future as the site has "fairly large commercial applications".
In an interview with TechCrunch, she said that investors had already shown an interest, although she said that there were no plans to roll out advertising on the site, or turn it into a political mouthpiece.
Menshn.com launches in the US with three topics of discussion - the US election, Barack Obama's campaign, and Mitt Romney's bid for the White House.
Users can join chats and post messages of 180 characters, rather than Twitter's 140 maximum. They can also subscribe to others on the site, or block them.
Any popular posts will be given greater prominence on the site, and people just signing up to Menshn.com will automatically follow 100 people who have been deemed notable.
Principles of gamification have also been incorporated on the site, as users can attract an 'up rating' for their "menshns".
They get one point for each rating, five points for someone who subscribes to them, five points for favouriting a room and 10 points for inviting a friend to the site. The top scorers will be displayed and users can also attract undisclosed "rewards".