Yes, but you may not love the experience.....
The 2014 Mac Mini's are only capable of 4K resolution at 52hz. 60hz is not possible. Further your only choices that will work are Full 3840x2180 or "retina" 1920x1080. You won't be able to use a "retina" 2560x1440 (doubling of the pixels each direction) on the monitor which I think would be ideal at 28".
So if you want to use native resolutions you are either stuck with super small icons and text at 4K or super huge "retina" 1080P and at only 52hz.