No. A 2007 Mini Cooper did not use a CVT transmission. It relied on traditional manual or automatic gearboxes instead.
To understand the question in context, the 2007 Mini lineup (the first-generation models known as the R50/R53) did not include a continuously variable transmission. Instead, buyers chose between a manual gearbox or a conventional automatic. CVTs were not offered for the 2007 Mini Cooper, and that remained true for this early generation of MINI cars.
What transmissions were available in 2007?
In 2007, MINI offered two broad transmission paths: a manual gearbox and a conventional automatic. The manual options were standard for many trims, while the automatic was a traditional non-CVT unit. There was no CVT option in the 2007 model year.
For prospective buyers or owners of a used 2007 Mini, this means you should expect either a manual transmission or a conventional automatic, but not a CVT.
Summary
No, a 2007 Mini Cooper does not have a CVT transmission. It uses a manual or conventional automatic gearbox, with no CVT option in that model year.