Titan Mauler does not remove the limitations for wielding oversized weapons, only the penalties.
Therefore, a Large Titan Mauler cannot ever wield a two-handed Huge, Gargantuan, or Colossal weapon.
A Large Titan Mauler can wield a one-handed Huge weapon as a two-handed weapon (and a light Huge weapon as a one-handed weapon.
A Large Titan Mauler can wield a light Gargantuan weapon as a two-handed weapon.
What a Large Titan Mauler is looking for is either a Gargantuan Aklys to be wielded as two-handed weapon of 4d6 damage, or a Huge bastard sword/dwarven waraxe to be wielded as two-handed weapon of 3d8 damage. Both options require Exotic proficiency.