From SmashWiki, the Super Smash Bros. wiki
Smashdown (全員バトル, Everyone Battle) is a multiplayer mode in Super Smash Bros. Ultimate. In it, after a character has been used, that character is not able to be chosen again for the remainder of the mode. It is one of two modes revealed so far for the game's Special Smash mode, the other being Custom Smash.
Each player chooses a different character and participates in a standard Smash battle (how much players can customize battle rules in Smashdown has yet to be seen). After the battle ends, the characters used are rendered unavailable for the remaining matches.