No, the rule for Combining Game Effects says that s of the same name don't stack effects while they overlap.
“Different game features can
affect a target at the same time. But when two or more game features have the same name, only the effects of one of them—the most potent one—apply while the durations of the effects overlap. For example, if a target is ignited by a fire elemental’s Fire Form trait, the ongoing fire damage doesn’t increase if the burning target is subjected to that trait again. Game features include spells,
class features, feats, racial traits, monster abilities, and magic items. See the related rule in the ‘Combining Magical Effects’ section of chapter 10 in the Player’s Handbook.
Similar to the fire example, Cutting Words reads:
you learn how to use your wit to distract, confuse, and otherwise sap the confidence and competence of others.
You shouldn't be able to become "more distracted and confused" on a single attack.
But it is Instantaneous
Now, Cutting Words doesn't have a duration, but in the case of cutting words they are happening at the same time, so they are clearly over lapping as they are both happening when the attack is happening (not just same round 6 seconds, but as the effect is landing). It would be hard to argue that they aren't happening at the same time as they are both reactions to the same split second action.