If you want to keep Applications, goto the Applications-Folder and save them to an external Media.
Put the Install-DVD that came with your Mini or the $29 Snow Leopard DVD in the drive, press "C" while booting, start the installation until it asks you to pick the hard drive, go at the top menu bar to "Utilities"->"Disk Utility", select your old "Macintosh HD" or what ever it is called, select the "Delete" or "Erase" tab, whatever it is called in English, and click "Erase":
Choose "Erase disk in 35 Cycles":
Go out and have a cup of coffee, that takes a while. Close the Disk Utility and continue the installation.