A streamer named Riz recently asked the Diablo IV officials on Twitter about the punishment for PVP deaths in Hardcore mode. Global community development director Adam Fletcher confirmed that the punishment for death in this mode will be permanent (permadeath), meaning that the player will have to start the game over with a new character. However, most players would avoid the Hardcore mode as it's not for everyone, so regular players do not need to worry about being permanently killed in-game.
By the way, Diablo IV will run a server stress test from May 13 at 3 AM to May 15 at the same time (GMT+8) for players to experience the game again. The full game is scheduled to be officially released on June 6 for Playstation 4 / Playstation 5 / Xbox One / Xbox Series / Battle.Net.