Depending on the nature of the editing you're doing, and the nature of your source material, a Mac mini may be more then enough.
A key is tho you need to use a modern Mac mini with a 9400m or better graphics chipset in it - the intel GMA chipsets are not supported and require workarounds to even install the software
I say *may* be because a lot depends on what you're working with etc.
I know I have edited on a Mac mini (the Mac mini that is now my home theater Mac); footage from a Canon HF100 (AVCHD, 17mbps avg data rate) transcoded into ProRES422 and it worked fine (I didn't use more then a couple of simultaneous video streams and depending on what effects I wanted sometimes I did have to deal with rendering) using a FW800 external drive for scratch.
Some functionality in Color will not work, if you use footage from cameras that have extremely high bitrates (a lot higher then the 20-24mbps on consumer camcorders) you may exceed your systems capabilities, motion projects may be limited on complexity and length.
I would also stay away from ProRES 444. You might want to use ProRES 422 Proxy or ProRES 422 LT for better performance on a mini tho. Here's a little blurp about the ProRES versions:
Apple - Final Cut Studio - Final Cut Pro 7 - Expanded ProRes
And if you notice under Proxy they refer to editing on a Macbook or MBP - the current mini is really about the same capabilities level of a the Macbook back when they wrote that (both machines had 9400m graphics, cpu close to the same (within a few hundred MHz), etc. - now the two machines are a little more separate as the gpu in the laptop is much more powerful then in the mini currently).
There are some nay-sayers that state that it won't work, but in all honesty, it does.
