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.
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.