That's more than overwatering.....Looks fungal to me...or viral. I think I would dig it out and toss it and sterilise the shovel and pour clorox in the hole...
Looks like the "Creeping crud"! LOL!
Linda C

Poor thing, yes it is very sick. I would give up on it. It looks as tho whatever is getting that may be starting to go after some of your other plants nearby it.

Have you seen any botrytis in the garden? Or is there any chance a high N fertilizer got near it?
I got something like this in one area that should have been perfect for sedums and lost Autumn Joy 2 yrs in a row. Then it killed Neon. Now there's a creeping sedum thats ok in that location. I think what happened is that lawn fertilizer was spilled in a bed that drains into this area and the super high N concentration was ok for pachysandra and Euonymous but too much for a sedum.
Alternatively - it is really sick with a nasty thing that rots out sedums and the location is contaminated with alien particles.

No doubt you need to yank that thing along with a good bit of the soil around it and replace it with a new soil.

This has happened to SOME of my Sedum AJs SEVERAL times in the last 10 years, usually when the spring or early summer has been too wet. All it takes (in my heavy soil) is a little bit of a low spot or some extra runoff or rain and this will happen.

Just chop off the tops that aren't mushy, dig out the rest of the plant & toss, add some new loose soil, maybe a little gravel, raise the planting area a bit and replant the tops. I've never cleared out the whole soil area, just amended it and raised it some & the new plants root and take off again.

If it happens again to the same plant or in the same area, then you might consider a new planting spot for the sedums and something more wet tolerant where they are now, but I have found it to be an occasional thing that happens to sedums in my garden. OTOH, I rarely have to water things :~) Good Luck with rescuing your sedums.

Thank you very much for the responses. I do have Sedum AJ in several spots in the garden. This thing happens only in one spot. I'll take care of it soon.

BTW, Leslie, your garden is absolutely beautiful. Mine will never be as pretty, because I like to cram plants in anywhere I happen to have a spot. lol.