Solution 1:

You need the 2.5 Ghz Mac Mini, which indeed also comes with an AMD Radeon HD 6630M instead of the integrated Intel HD Graphics 3000 on the 2.3Ghz model.

For a list of models that support up to two Thunderbolt displays connected, check this support article over on the Apple website:

Thunderbolt ports and displays: Frequently asked questions (FAQ)

  • 14 - How many Apple Thunderbolt Displays can I use with my Mac in OS X?