Suppose an attack does 5 piercing and 5 poison damage (or 5 slashing and 5 fire, etc.) and the player parries the attack, and rolls to reduce 6 points of damage. Which type of damage is reduced first? Would the answer be different if it were 9 weapon damage and 1 elemental, or vice versa?
When another creature damages you with a melee attack, you can use your reaction and expend one superiority die to reduce the damage by the number you roll on your superiority die + your Dexterity modifier.
This matters if, for example, the character has resistance to one of the damage types.
The kindest interpretation (and one that does make some "sense") would be that it reduces weapon damage first, and if it reduces the weapon damage to zero, none of the additional damage is done either, but that seems over powered. Unless someone can unambiguously point me to rules that support this interpretation, I prefer an interpretation where the total damage reduced is as rolled.