The rules use a certain pattern when discussing modifiers and Cutting Words adheres to that pattern. It is therefore a modifier to a roll result and does not replace the result.
Almost without fail:
If a modifier is a fixed value, the rules use the words "modifier" and "penalty."
See Raise Dead, Resurrection, Slow, Alter Self, Haste, Magic Weapon, Pass Without Trace, Shield, Shield of Faith, Slow, Warding Bond, many Clerics' Channel Divinity abilities, among others.
If the modifier is a variable value resulting from a die roll, the rules use the wording "roll a [die] and [add/subtract] the result" from the d20 roll.
See Bane, Wild magic results 11-12 and 35-36, several Battlemaster Fighter's maneuvers, and others.
I didn't do an exhaustive search through the rules text but I was only able to come up with one instance where the rules break this pattern: Wild Magic Sorcerer's Bend Luck:
roll 1d4 and apply the number rolled as a bonus or penalty (your choice) to the creature's roll.
User Medix also located the Unearthed Arcana Brute Fighter's Brutish Durability:
Whenever you make a saving throw, roll 1d6 and add the die to your saving throw total. If applying this bonus to a death saving throw increases the total to 20 or higher, you gain the benefits of rolling a 20 on the d20.
This ability is worded very similarly to Cutting Words (roll ... add to roll/throw) except that it explicitly addresses the interaction with rolling an adjusted 20 or higher. Keeping in mind the general adage that "Spells (and abilities) do only what they say they do," this suggests the that Cutting Words' lack of a similar addendum further supports the interpretation that it may not cancel a critical roll.
So with the one exception of the Wild Magic Sorcerer, the book seems to refer to modifiers in a consistent pattern. This combines with the general rules for making an attack or check which states that, when determining modifiers, the following are considered:
In addition, spells, special abilities, and other effects can apply penalties or bonuses to your attack roll.
If we subscribe to the interpretation that the word "modifier" must appear in the rules text in order to qualify a change to a d20 roll as a modifier, otherwise it counts as the natural roll result itself, then we must extend this logic to a number of other abilities/spells that use the same wording for variable affects to a die roll.
I do not believe that is the correct interpretation. Instead, things that change (ie modify) the roll result are modifiers unless the rule explicitly says they function in some other way. Examples of this include dis/advantage, the Lucky feat (or Halfling racial), Wizard's Portent, all of which state that the player chooses which roll result to use and/or replaces (keyword) another result.