Would Fey Ancestry affect Cutting Words?

Question

Now, I know that Cutting Words is inferred to be a Charm effect based on the last sentence of the paragraph. This raises a question for me; would Fey Ancestry affect Cutting Words? (I.e. reducing the effect somehow?)

Answer 1

No

There are no secret rules

Fey Ancestry: You have advantage on Saving Throws against being Charmed, and magic can’t put you to sleep.

There is no saving throw for Cutting Words and it doesn’t put you to sleep so Fey Ancestry does nothing here.

Answer 2

No

Cutting words says:

...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...The creature is immune if it can’t hear you or if it’s immune to being charmed.

Since Cutting words explicitly says that it cannot be used against creatures immune to charm, it certainly is tempting to think of it as a 'charm effect' or infer that it 'charms' the target.

However, in response to the question 'which spells/effects are actually charms, anything from enchantment school?', Jeremy Crawford has said:

Being charmed means being subjected to the charmed condition.

and he has also said:

Fey Ancestry benefits any saving throw meant to stop an elf from suffering the charmed condition.

This means that when Fey Ancestry says:

You have advantage on saving throws against being charmed, and magic can’t put you to sleep

it means that you have advantage on saving throws against any effect that imposes the Charmed condition, only.¹

Cutting words does not impose the Charmed condition, so RAI it does not count as 'being charmed'. Rather than inferring 'Cutting Words must be a charm effect', we instead have to infer that 'Since Cutting Words cannot affect creatures immune to charm, but it is itself not a charm, then creatures immune to charm must also have the unstated ² property of being immune to Cutting Words as well'.

Now, Jeremy's Crawford's tweets are not official rules statements. You might not be convinced that RAW being charmed means being subjected to the charmed condition, only. You might still believe that Cutting Words is some sort of charm effect. However, even if it is, it is also undeniably an effect that does not permit a saving throw, and thus as Dale M says, Fey Ancestry does nothing to protect you since it covers only charm effects that permit saves.

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¹_{Note that the word "charmed" in the D&D beyond description of Fey Ancestry links directly to the Charmed condition.}

²_{Is this a secret rule? No, not really. Just one that is difficult to find.}

Answer 3

No.

Cutting words doesn't work on creatures ~immune to charm~. This is the last sentence of the paragraph you mentioned.

The creature is immune if it can’t hear you or if it’s immune to being charmed.

Those who are merely resistant or enjoy advantage or a bonus to their saves (against charm effects) have no special protection.

The game has degrees of protection. Someone only resistant to fire might find detrimental to their health to swim in lava (an argument can be made that not even those immune can swim in it, unless they are very heavy - lava is too dense).