My first guess is that the slow down is due to Photoshop trying to save to a USB external drive, and not a bad installation of Photoshop (illegal perhaps, but not corrupted). The USB connection between the Mini and external HDD is slow, so it can take some time to move all those bits over the wire.
However, lets look at some other stuff just be sure.
There is an application on your system called Activity Monitor. You can find it in Applications > Utilities Or, you can just do a search for it with Spotlight... whatever you find more convenient.
One of the tabs in Activity Monitor is System Memory. There is an info panel below, with graphs and colours and stuff. We will want to see that. Also, above that, there is dynamic list of 'processes' being run. One of the column headings is called 'Real Mem' (for Real Memory). Click the column heading. This will sort that column in biggest to smallest, or vice versa. Clicking the column heading toggles between biggest or smallest at the top. We want the biggest numbers at the top.
The next time Photoshop is grinding away. Open this page of Activity Monitor, and post the screen shot. Thanks.
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With that done... now let me get preachy for a moment. Please spend the time (and money) it takes to get a licensed version of a photo editor. We, as creators of intellectual property (that is easy to steal), ask that other people respect our rights and pay us for the content we create. We should in return have the same respect for other people who create content - in this case Adobe.
There are other free or inexpensive editing programs. I hear Pixelmator recommended very highly and very often. Most non-professionals don't need the full power of Adobes's CS suite. There is the much more affordable Photoshop Elements if you need an Adobe product. Or, perhaps you qualify for an educational license - which is a phenomenal deal for the CS package.