Is there any reason(s) when luggage is screened at airport security, not to be able to take a Mac Mini, keyboard and mouse as carry-on luggage aboard an aircraft ?
No reason at all. You do not have to take any of those items out of a bag going through x-ray like you do a laptop (go figure) and TSA is familiar with them. You might consider taking the Mac mini out or packing it in such a way that it will show up easily on x-ray.
I'd say you're good to go.
I travel often with an iPad, iPhone, MacBook Pro and all associated power supplies and chargers as well as a small external hard disk. I take the MacBook Pro out and put it in a bin but the rest of it stays in my pack. Occasionally a TSA agent will want to look in the pack but that's rare and usually because the stuff was so densely packed they couldn't visually sort it out on their monitor.
While I don't have personal experience with a Mac mini, my guess is you'll be just fine. When in doubt, making it easier for TSA to see it by taking it out and putting it in a tray. If you have a small padded case it can travel in, you can leave it in that but take it out of your larger pack or suitcase so they can scan it separately but I'm betting that won't be necessary.
All of that said, every airport/TSA station is different and some are tougher than others. I travel out of Hartford, JFK and LAX and they can all be tough but I've never had an issue.