Hi Carolina Mtn Gardener,
I'm not finding much info on insect pests and sedum.* You obviously have the larval stage of some pest.* I do find reference to black vine weevils, but the feeding habits of the larvae are to feed on the roots.* The adults do notch the edges of the leaves of plants, often making them look scalloped.* Do you see anything like that?
http://www.agnr.umd.edu/MCE/Publications/PDFs/FS805.pdf
Here's a root weevil grub on a sedum.
http://www.entomology.wisc.edu/insec...t_info.php?369
Here's the damage.
http://www.entomology.wisc.edu/insec...t_info.php?370
I would definitely cut off the stems of any infected plants and destroy them.
Newt
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.