Q: Delete faulty mac mini hard drive

- If you can still boot the old Mini and you have another Mac you can connect the two via FireWire and the boot the old one in Target Disk Mode

How to use and troubleshoot FireWire target disk mode - Apple Support

You can then access the HD on the old Mini. Make sure you use a secure erase. That overwrites the date. A simple erase just deletes the directly.

- Otherwise you will have to disassemble the old Mini. For how see:

http://eshop.macsales.com/shop/mac-mini/

Place the HS in a external enclosure and erase the HD. Or you can just keep the HD yourself