Cutting Words applies after resistance because it is not damage reduction, it is subtraction with unique and explicit behaviour.
The text of Cutting Words:
When a creature that you can see within 60 feet of you makes an attack roll, an ability check, or a damage roll, you can use your reaction to expend one of your uses of Bardic Inspiration, rolling a Bardic Inspiration die and subtracting the number rolled from the creature’s roll. You can choose to use this feature after the creature makes its roll, but before the DM determines whether the attack roll or ability check succeeds or fails, or before the creature deals its damage.
Subtract is unique language
The term subtract is incredibly rare in DnD5e. It is used 9 times in the entire basic rules. It is only ever used when referring to the mathematical operation;
- "For disadvantage, subtract 5 [from a passive skill check]"
- "To determine an ability modifier without consulting the table,
subtract 10 from the ability score and then divide the result by 2
- "Whenever a creature takes damage, that damage is
subtracted from its hit points.", etc.
The term "subtract" should not be understood as the gameplay mechanic reduce damage. In no instance is it ever used that way.
This is conclusive enough by itself, however people have various preconceptions that should be dismissed.
With all other uses of the Cutting Words the subtraction happens "before the DM determines whether the [roll] succeeds or fails". This is after all modifications and other effects have been applied, right before the DM resolves the roll.
This also matches up with the mechanics on how to handle other roles: "before the DM resolves the roll". This applies to damage rolls which is why they chose the unique term "subtracting" to distance it from existing mechanics and prevent confusion. The timing of the skill, "before the creature deals its damage", is explicitly mentioned. This is unusual because if this was a normal 'damage reduction' then the timing is already defined in the Combat rules, and this is not where it would happen. Normal 'damage reduction' happens "before resistance and weakness is applied".
"before the creature deals its damage"
What exactly does "deals its damage" mean? This isn't a normal choice of words. This phrase is used in a lot of contexts but the exact meaning often isn't clear. "Swords deal slashing damage", "an attack deals 5 damage".
The rules for Object Armor Class provides a hint:
An object's Armor Class is a measure of how difficult it is to deal damage to the object when striking it (because the object has no chance of dodging out of the way).
This suggests "dealing damage" does not mean rolling AC, which is a start.
Knocking A Creature Out says:
When an attacker reduces a creature to 0 hit points with a melee attack, the attacker can knock the creature out. The attacker can make this choice the instant the damage is dealt.
This seems to say that "damage is dealt" is when the damage is applied. That is to say, after rolling damage you can choose to knock the creature out, you don't do it before rolling damage.
Where does this fall in the rules for Making An Attack:
Choose a target. Pick a target within your attack's range: a creature, an object, or a location.
Determine modifiers. The DM determines whether the target has cover and whether you have advantage or disadvantage against the target. In addition, spells, special abilities, and other effects can apply penalties or bonuses to your attack roll.
Resolve the attack. You make the attack roll. On a hit, you roll damage, unless the particular attack has rules that specify otherwise. Some attacks cause special effects in addition to or instead of damage.
In most circumstances resistances are the last thing to be resolved. However, the specific overrules the general, and the text "before the creature deals its damage" can be interpreted as "directly before the creature deals (ie reduces the hp of the target) its damage". As opposed to if the text read "after damage is rolled".
The DM deals the damage in step 3. This is after all resistance and reduction is applied. Cutting Words is a special case subtraction that does not follow the normal rules, which is why it has special, unique wording. It is intended to modify the damage roll directly before Step 3.