We already know from Sage Advice and other answers to other questions that by RAI, (and I guess RAW too), Cutting Words (and Bane) don't work on critical hits, though in the case of Cutting Words they can still reduce the damage by an amount.
The Grave Domain's 6th level feature, Sentinel at Death's Door states that:
As a reaction when you or a creature you can see within 30 feet of you suffers a critical hit, you can turn that hit into a normal hit. Any effects triggered by a critical hit are canceled.
Does that mean that, since it is no longer a critical hit, that Cutting Words can now apply to it properly?
A follow up question: If the above is true then if a Bard cast Cutting Words before the Cleric used Sentinel at Death's Door on a critical hit, does Cutting Words still apply?