These two features probably shouldn't combine to cause a critical hit to miss
1. 'Rules as Written' it's arguably possible:
As quoted in your question, Sentinel at Death's Door, turns a critical hit into a normal hit.
Cutting Words can be used:
[...] 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. (emphasis mine)
Under normal circumstances an attack roll of 20 will always succeed:
If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target's AC. This is called a critical hit [...]
So, if a critical hit 'hits regardless of any modifiers or the target's AC' the fact that this is no longer a critical hit means it no longer 'hits regardless of any modifiers or the target's AC' and is now a viable target for cutting words.
Cutting words could not have been applied 'after the creature makes its roll, but before the DM determines whether the attack roll or ability check succeeds or fails' because as soon as a 20 was rolled it was classed as a critical hit and the DM did not need to determine whether it would succeed or fail - it was an automatic success.
However, once the Grave domain cleric has used their reaction to negate the critical hit there is a second opportunity to use Cutting Words 'before the creature deals its damage'. So, now the Lore Bard can use Cutting Words to try and cause the attack to miss.
2. However, it's probably against 'Rules as Intended':
The full text for Cutting Words states:
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 die and subtracting the number rolled from the creature’s roll. 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.
So, three types of rolls can be affected:
- attack rolls;
- ability checks; and
- damage rolls.
And the point at which they can be affected is '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'.
It's not completely explicit, but it is pretty suggestive that 'attack rolls' and 'ability checks' are the rolls than can be affected by Cutting Words' 'before the DM determines whether the attack roll or ability check succeeds or fails', whereas the damage roll is the roll that can be affected when hit has already been determined but 'before the creature deals its damage' - meaning the attack roll cannot be retroactively affected after hit has been determined, but before damage has been rolled.
Read this way the rules would definitely prevent Sentinel at Death's Door and Cutting Words from combiing in order to make a critical hit miss.
3. Either way, if you allow this combination is it balanced?
Allowing this will not break your game, as it has quite a high 'opportunity cost' - to be honest it's probably actually an inefficient use of your players resources.
The party will require both a Grave domain Cleric (level 6) and a Lore Bard (level 3) to have access to both of these features. Both abilities consume each player's reaction so a multiclass Cleric/Bard could not do this on their own. Sentinel at Death's Door can be used a limited number of times per long rest and Cutting Words spends one use of Bardic Inspiration die.
Cutting Words used this way also has a higher than average degree of failure. By which I mean that, statistically, the Bard will likely have to roll pretty high on their Bardic Inspiration die, in order to cancel a hit from a 20 on the dice, plus any modifiers the attacker adds, in order to bring the total below the AC of the attack's target.
A Bard who is playing the percentages might prefer to save their Bardic Inspiration to use when it is statistically most likely to cancel damage.