Potentially the number on the d20, but not the total or the outcome
As noted in Bloodcinder's answer, official 5e rules designer Jeremy Crawford answered a related question on Twitter about the College of Valor bard's Combat Inspiration feature (PHB, p. 55), which specifies that it can be used "after seeing the roll but before knowing whether it hits or misses":
Bard Combat Inspiration use with reaction to add the roll to AC "AFTER SEEING THE ROLL" So DM must show his roll to player?
If a player character ability relies on knowing a monster's roll, a DM may say what the roll is or show it
Master @JeremyECrawford, you intended that DM must communicate only the number on the dice (without added any modifiers), right?
The same or similar logic could be applied to the College of Lore bard's Cutting Words feature, though it's important to note that Cutting Words' description is slightly different.
Whereas the Valor bard's Combat Inspiration feature says:
Alternatively, when an attack roll is made against the creature, it can use its reaction to roll the Bardic Inspiration die and add the number rolled to its AC against that attack, after seeing the roll but before knowing whether it hits or misses.
The Lore bard's Cutting Words feature says:
You can choose to use this feature after the creature makes its roll, but before the DM determines whether the attack roll or ability check succeeds or fails, or before the creature deals its damage.
Cutting Words doesn't explicitly state what the player knows about the roll, but the fact that you can wait until after the roll is made but before the outcome is known suggests that you know something about the roll.
If we apply the same logic given in Crawford's tweets above, the DM would likely say or show the number on the d20, but not announce the modifiers or total until after the bard decides whether or not to use Cutting Words. (The DM and/or other players may feel that this slows the game down unnecessarily in practice, so your table might choose to run it a bit differently.)
The 2019 Sage Advice Compendium also explicitly addresses this question and a related one:
Is the intent that a bard gets to know the number rolled on an attack roll or ability check before using Cutting Words, or should they always guess? If used on a damage roll, does Cutting Words apply to any kind of damage roll including an auto-hit spell like magic missile?
You can wait to use Cutting Words after the roll, but you must commit to doing so before you know for sure whether the total of the roll or check is a success or a failure. You can use Cutting Words to reduce the damage from any effect that calls for a damage roll (including magic missile) even if the damage roll is not preceded by an attack roll.
It avoids overtly saying whether the Lore bard sees or is told the number on the d20 before using Cutting Words, but does reiterate that they can wait until after the roll to make their decision on whether to use it. This again suggests that they do know something about the roll, but not the overall outcome.
Your interpretation of knowing the outcome explicitly contradicts the feature description of Cutting Words; your DM's interpretation that you know nothing about the roll is theoretically possible if sticking purely to RAW, but seems absurd given that you can wait until after the roll is made to use it. It seems like you and your DM arrived at Crawford's recommended solution to the matter entirely by coincidence, by meeting in the middle.