Here's how to do it:
1. After you die, do not hit the "Delete World" button, you need to just close Minecraft. If you do happen to accidentally hit the "Delete World" button you will not be able restore it with this method, I will explain a method on how to do that after.
2. Go to http://mc.42nex.us/ and get your seed of your hardcore world, you may want to write this down.
3. Start a new Hardcore/Survival/Creative world, the option you choose here will be the way your Hardcore world will be after restoration, and use the seed to your hardcore mode world, and create the world.
4. If your spawn point is not the same as your Hardcore mode world then you may want to change it with a program like lolEdit or MCEdit
5. After your spawn has been changed (if needed), then open up your saves folder (start>run>"%appdata%\.minecraft\saves") and locate your old Hardcore mode world and the world you just created.
6. Copy the "level.dat" and "level.dat_old" files from the new world to the old Hardcore mode world, you may want to back-up the files before overwriting them though.
7. Log in to Minecraft and open up your old Hardcore mode world and you should be back at spawn with nothing, just as if you died in Survival.
If you already hit the delete world button you may be able to find a Windows-made backup of it, right-click on your saves folder, hit properties, then go to Previous Versions and choose the newest version that was before you died, then click open. You should find your Hardcore world in there and copy it over to the saves folder. This will restore a previous version of your world, you may lose some stuff, but you should keep most of the major stuff, and as far as I know this only works with Windows.
I hope this helped.