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Cutting Words says (PHB, p. 54, emphasis mine):

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 and substracting the number rolled from the creature's roll.

Now, if a bard uses Cutting Words in order to alter the damage roll of a creature throwing some AoE at the party (a wizard casting a Fireball, a dragon's breath weapon, etc.), does it "cut" the damage done to each target affected by the AoE effect?

That would seem pretty powerful, considering that a 5th level Lore bard with a charisma of 18 can use Cutting Words once per round, up to 4 times between each short rest, using d8s to "cut" the damage done by those effects.

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Yes, Cutting Words Reduces AoE Damage Rolls

As you quoted, any damage roll can be reduced. While this may seem powerful—reducing a fireball's damage by 1d8—it's not very.

At 5th level, a bard can use cutting word 4 times for 1d8 each time but a fireball at 5th level is doing 8d6 damage. Compared to 8d6, 1d8 reduction isn't that big of a deal.

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    \$\begingroup\$ Too be fair, if you have 6 players in the AoE, it is 1d8 times 6 of damage that is averted, nearly an equivalent of (avg) superior healing potion (8d4+8), which can be very, very expensive item. Or, three cutting words equal a Mass Cure Wounds, more or less. Though if your players stay in a fireball AoE for 3 turns, they have bigger problems ;) \$\endgroup\$
    – Gerino
    Sep 6, 2016 at 15:50
  • \$\begingroup\$ While true, cutting words is a reactive damage mitigation, not a proactive damage reversal. In order to use cutting words, damage has to already have been rolled. A potion can be quaffed at any time. Also, a potion is more potent because all 8d4+8 healing is applied to one character. \$\endgroup\$
    – Christopher
    Sep 6, 2016 at 17:03
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    \$\begingroup\$ Comparing it to a potion is a little bit of a bad comparison. It should be compared to other uses of a bardic inspiration die. Should I reduce this fireball by 1d8, or should I potentially cause one attack to miss? Unless that one attack is fairly large, the use against a fireball is effective use of a die. \$\endgroup\$
    – Derek Stucki
    Sep 6, 2016 at 19:19
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    \$\begingroup\$ You're right. After some calculations, I've found that CW using a d8 mitigates 4%-29% (avg. 16%) of a Fireball's damage, which is much less than, say, the 50% spell damage reduction provided by the Oath of the Ancients Paladin's Aura of Warding (not to mention the Aura of protection already granted as a lvl 6 class feature, stacking on it). So not that big of a deal after all. \$\endgroup\$
    – Meta4ic
    Sep 6, 2016 at 21:43
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    \$\begingroup\$ worth noting that it affects the damage roll directly, which means that it's before vulnerability/resistance/etc. \$\endgroup\$
    – Ben Barden
    May 31, 2019 at 18:42

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