In Team Deathmatch there's an option to disable players talking to living ones when they're dead. This includes when you've ran out of lives or just during the respawn time.
It'd be possible to remove the death notices by packaging GameConnection::onDeath. Look at any mods using the 'special kill notices' script (Push Broom Reflector, Shield, Amade's Bots, Assist Kills) as that clears the damage type so the default message doesn't show up if it's been modified.