You cannot delete the address: it, and if you have it, the @me.com address are the same thing and are the primary address of the account.
Other than making an alias (which would behave exactly like a separate address excepting only that it delivers into the same inbox as the primary address) the only way to get a new @icloud.com address is to create a new Apple ID (for which you will need a different non-Apple address) and use it to create a completely new iCloud account from scratch.
The only way to create a new iCloud email address, is to create a new iCloud account from a totally seperate AppleID.
You can delete your current iCloud account by just deleting from Setting > iCloud on your iOS device and from the iCloud system preferences pane or control panel on your computer.
Make sure you backup any data you want to keep, before deleting the account.