I don't have the specs of the new mac mini, but I have tried the trial of FCP on my 2.4 MBP 8GB RAM, 5400 rpm 1 TB drive. The experience was miserable. When I upgrade, I will be sure to have a discrete video card instead of the integrated graphics. It doesn't look like you can configure the new mini that way. You're stuck with integrated graphics, but you do have thunderbolt. You could conceivably use a really fast drive as a scratch disc and not be bottlenecked.
If it were me, I wouldn't try it. If you have an Apple store near by, try it out there, first.