Displacer Beasts have a Tentacle attack that does 7 (1d6 + 4) bludgeoning damage plus 3 (1d6) piercing damage. Does the bludgeoning and piercing damage reduction granted by Heavy Armor Master reduce that total damage by 6 or 3? If only 3, what determines which of the two damage types is reduced?
Yes, due to the wording of Heavy Armor Master
From the PHB, the feat is as listed:
While you are wearing heavy armor, bludgeoning, piercing, and slashing damage that you take from non magical weapons is reduced by 3.
If you separate these out into three separate statements (all are true, because they are engulfed within an "and" statement), they are as follows:
- Bludgeoning damage (from nonmagical weapons) is reduced by 3.
- Piercing damage (from nonmagical weapons) is reduced by 3.
- Slashing damage (from nonmagical weapons) is reduced by 3.
Then it stands to reason that each damage type would be reduced within that attack. This is my reasoning, as that is how and and or work in logical statements. If it was "Bludgeoning, Piercing, or Slashing" then it would only count once, no matter how many damage types were present.
The rules as they are provide no further clarification for this case.
This has caused issues in the past. A Parry was used to reduce the damage of a multi-faceted attack with differing damage types. Seeing as a character could have resistance to one of the types, and resistances are applied after all other modifiers, it would be important to know which part of the attack would the Parry reduce (to calculate the total reduction). The only official response we have for that particular case is "let the player decide".
As with any situation not defined by the rules, the DM has the final word. He can choose to treat damage reduction for each type separately, allow reducing only one type, or let the player roll for a chance to reduce both types. And if the player can reduce only one type of damage (because of the DM's ruling or a failed roll), they get to choose which damage type to reduce (in conjunction with the linked answer above).
If you would like something more concrete, though, I will present an argument that damage reduction should be done separately per damage type. In your case that would be 3 for the bludgeoning part and up to 3 for the piercing part of the attack (depending on the 1d6 roll, if rolled).
Let's say you were being attacked by a flying snake (used as an example in this question with similar issues). The snake deals 1 piercing damage and 3d4 poison damage. Naturally, your mastery of heavy armor does nothing about the poison, but it can surely reduce piercing damage! So the feat is used... but it doesn't seem right that it would take away the full 3 damage. Only 1 damage was piercing. So we only take away 1 damage, and by extension we rule that you cannot reduce the total damage of a multi-faceted attack with different damage types if only one part of the attack deals damage that you can reduce.
We observe a similar situation with resistances. Resistances halve the damage of their respective type. If an attack consists of multiple damage types, your resistance only applies to the part of the attack that you're resistant to. Fire resistance means you don't have to worry much about the heat of a flaming sword, but that sharp edge is still gonna hurt.
So, if we apply damage reduction individually per damage type, there's no reason we shouldn't do that when an attack contains multiple damage types that we can reduce.
Again, with resistances, it's clear: if you resist only one damage type, halve the damage of that type. If you resist both types, halve the entire attack. There's not much difference in halving each type individually and halving the total sum, only a point or so due to rounding down.
But with this feat, though, the difference is substantially greater. Is that a problem? The damage reduction from the feat becomes less relevant the further in level you go, and compared to actual resistance it's clearly inferior.
From a role-playing perspective, we view the attack as consistsing of two parts: a heavy hit of the tentacle and the pierce of its spikes. As a heavy armor master, you can move well enough in heavy armor to avoid taking full bludgeoning force, and you can aim to defend with a thicker part of your armor to lessen the effect of the piercing spikes.
Usually if the player has an effect that reduces one damage type to zero, and the second damage type is a consequence of the first, I count the attack as deflected, and the poison is not applied as if the player were immune, because poison is an effect. Similar to how Ray of Frost does not slow an Aburation wizard if their ward does not let any damage through. And the tentacle monster can attack with those damage types, but obviously it cannot pierce and bludgeon with the same tentacle. Therefore, those are separate attacks and reduced seperately.