Is it possible to order a new Mac mini with an Nvidia graphics card?
No you can't order the current generation Mac Mini Mid-2011 with anything other than what Apple will offer to you as a build to order option for graphcis.

Currently the only options for graphics on the Mac Mini are:


Intel HD Graphics 3000
AMD Radeon HD 6630M


Recall from iFixit's Mac Mini tear down that the Mac Mini is a highly integrated machine, and there really is no such thing as a "graphics card" in it, its a graphics chip set on the motherboard as pictured below from iFixit, what Apple puts on it is what you have to choose from. 



However, with the Availability of Thunderbolt there is opportunity for expensive external graphics options on Mac Mini's with Thunderbolt. Products such as the Sonnet Echo Express offer external PCI express x4 speed slots, but as of yet there are not listed graphics card that are compatible.