They would stack because they have no duration
The rules on stacking/combining game effects states (page 252):
[W]hen 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
I would argue that modifiers to rolls do not actually have a duration and so they cannot actually overlap, so the clause about stacking effects won't apply.
This is similar to the answer to a related question about simultaneous fireballs which argues that you would take damage twice because the spells (and their damage) are instantaneous effects without duration.
Similarly the modifier of Cutting Words does not have any sort of persisting effect that you could call a duration, it simply happens. The modifiers do not have any sort of duration whatsoever, so they cannot overlap. Thus the rules on overlapping effects do not apply and the two uses of Cutting Words will stack.
The Essentials Kits explicitly defines what a duration is, Cutting Words would stack with itself
The Essentials Kit (page 3) states:
[...] When two or more effects have the same proper name, only one of them applies while the durations of the effects overlap (a duration is a time span of 1 round or more). The most potent effect--such as the highest bonus--is the one that applies, or the most recent effect applies if the effects are equally potent. For example, if bless spell is cast on you when you're still under the effect of an earlier bless, you gain the benefit of only one casting.
Because Cutting Words does not last for "a time span of 1 round or more" the rule on effects with the same name cannot apply. Thus they stack.