Good strategies above, but in addition:
In making an attempt to construct up their confidence, it sounds such as you is perhaps ascribing your worker’s detrimental self-talk to missing self-confidence. That is perhaps the case, or a big a part of it, however that additionally could also be outdoors of your capacity to affect as a supervisor: you’ll be able to’t change somebody’s perspective or worldview *for* them, they’ve bought to decide on to do this themself.

What’s squarely inside your scope to affect is the observable habits. You’ll be able to level out the sample like Cat in Boots’ remark describes. And you may inform your worker to chorus from making these detrimental feedback, simply as you’d anticipate them to chorus from making detrimental feedback a few coworker, or chorus from kicking the photocopier when it malfunctions. After which gently, firmly, constantly maintain them to that expectation till the habits modifications: every time they begin to badmouth themself, interrupt them, remind them of the expectation, and check out once more.

“Whoah, Cyril, I’ma cease you proper there. That’s precisely what we talked about. I didn’t say these issues, private judgements like that don’t belong in respectful skilled communications, and I received’t have you ever talking like that about one among my workers. Obtained it? (If they appear upset at this level it will be a kindness to supply: Do you want a minute to take that in and compose your self? or related, and look away or allow them to step out for a number of seconds or at most minutes, earlier than resuming the dialog). Let’s begin over with out judgmental feedback this time; you’re welcome to ask questions, although. As I used to be saying about these TPS Experiences: once you XYZ the PDQ, it’s worthwhile to bear in mind to ABC, as a result of DEF. Now, to verify we’re on the identical web page, are you able to summarize again to me the change in process from the way you’ve been doing it?”

Assuming you already acknowledge their success and progress/enchancment in varied features of their job {and professional} habits, proceed doing that — and add “not badmouthing themself when receiving suggestions” as a factor to acknowledge enchancment in. Don’t make an enormous congratulatory deal about it, however do discover once you’re capable of give them suggestions with out them saying one thing self-deprecating, and provides them a short “I observed how professionally you obtained suggestions this time” “thanks” or “I recognize your effort” or the like. It most likely goes with out saying to not lose your mood with them or say detrimental issues about them like they do about themself– that’ll simply “show” they have been “proper”. But it surely is perhaps extra counterintuitive: don’t argue towards the detrimental issues they are saying, don’t reassure them, or counter with positives after they deliver up the detrimental — that’s coaching them they will keep away from uncomfortable or impartial suggestions and procure reassurance by badmouthing themselves.

If that is one thing they’re capable of change simply based mostly on teaching from knowledgeable mentor, you need to see a change after a number of to a number of repetitions of the interrupt-correct-do-over, although they could have a tough time at first and the habits could even briefly enhance earlier than lowering.
If the habits persists regardless of teaching, inform them it’s an impediment to their skilled success, and counsel assets resembling EAP they will use to work on no matter no matter is stopping them from altering their habits.