Hardcore mode is a game mode variant of survival, differing primarily by the lack of the ability to respawn (instead, the world is deleted) and change difficulty.
While playing hardcore mode, the game is set to “hardcore” difficulty, which only differs from “hard” difficulty in that it cannot be changed to another difficulty while playing the world and you also cannot enable cheats or bonus chests. Also in that if the player dies, the world is deleted and the player is taken to the title screen. In the world selection screen, it will say that the world is in hardcore mode in bold, red letters, as a warning.
When the player dies, the game over screen only offers a button to delete the world save instead of survival mode’s Respawn and Title menu buttons. When you die, "Game Over! You cannot respawn in hardcore mode!" appears as well. The world save still exists until the button is pressed, leaving the opportunity for one to keep their world by using 3rd party tools. Exiting the client and loading the world again only reloads the game at the game over screen. However, you can go into the .minecraft folder and find the hardcore world save. Copy it before you die, paste it somewhere safe, and you can drag it back into the .minecraft folder to start the world from there.
Hardcore Mode has been made an option for multiplayer, and its functions are similar (more so since Single Player now runs on a multiplayer database). Dying while in the server does not give the player a respawn button, replaced with a button prompting the player to "Leave Server". When clicked, the player gets the message "You have died. Game over man, it's game over!", as well as: "Banned from server" "Reason: Death on hardcore". If you try to reconnect to the server, it says "You are banned from this server!".
It is possible for a server admin to allow a player to rejoin after death, but the admin will need to stop the server and edit server files: First, deleting the player data from (Map name)> players > (deadplayer).dat, then going into the banned-players.txt and erasing the relevant data under the index ( banned by | banned until | reason). The admin can then restart the server and the affected player can spawn again. However, the player will appear at the original spawn point with no items, armor, or levels (because their player data has been deleted).