Can I use my UK Mac Mini (Mid 2010)  in the US? I'm from England and I'll be going to the US and I'd like to take my Mac Mini (Mid 2010) (not the newest version).

My main question is: would it be safe to use over there?

I'm worried because of the voltage difference.

If so should I purchase a US power supply cable (does Apply even sell these separately) or a UK->US plug adapter?
Yes it is safe. You will need a US plug adapter or a replacement cord, but the mac itself is good to go.   

Reading through the specs it states:

Electrical and operating requirements
Line voltage: 100-240V AC

The power supply can handle both the frequency and voltage changes. 

And for the question about buying a power cable or use an adapter -> Up to you I did use both and didn't have any problems. I'd go for a US power cable since that is less clunky, if you stay for longer. If it's only for a few weeks I wouldn't bother buying a cable.