An Arena Attack doesn’t deal damage, but subjects both players to a deathrand.
The deathrand = [power of opponent]/(your toughness - damage you carry).
So e.g. a player with 10 toughness, who carries 6 damage already and is resolving an Arena attack with a player with 1 power, as attacker or defender, has 25% to die.
A player that is immune to (combat) damage or has relevant protection cannot be damaged and therefore cannot be killed by an Arena Attack.