A third way to do this, and my personal favorite, is the Add to Library function.
First, change your iTunes preferences so that iTunes does not automatically duplicate every song file you have and put it on your Mini's hard drive. Go to the iTunes menu > Preferences... click the "Advanced" Tab. In the advanced menu, uncheck the "Copy files to iTunes folder when adding to library" selection.
Then, connect your external hard drive, go File > Add To Library, then select the folder on the external drive that contains all your music.
The reason I prefer this method is that I can add files from any location, and it'll have them in the library, and won't move or copy files.