How do I switch it to Hardcore Mode in SMP?

According to the wiki, there's no option for it on servers. Hardcore isn't a difficulty, it's a separate gamemode, and the only options for that is creative and survival.

This kind of makes sense too. Since the world is deleted when the player dies, it'd be harder to handle it when there are multiple players, waiting until they're all dead. Also, no one could drop in, and what if all the players just disconnected, and someone else joined while they were gone and died?

In Minecraft 1.3.1 and later, you can simply edit your server.properties files.

Locate the line that says hardcore=false and change the false to true. Voilà!

If you use Bukkit 1.8.1, you can use this pretty plugin: Hardcore

It's not updated to 1.0.0 yet , but it probably will after RB of Bukkit get released.