There's nothing to be gained from removing healthy tissue. Try to remove rotten (soft, discolored) parts carefully from the healthy part that's left, because the rot will tend to spread otherwise.
For what it's worth, this is pretty much the prototypical Echeveria meltdown, which can come about for different reasons. Pretty advanced. I say this based on growing a couple dozen different kinds and some mistakes I made early on. If you do try again (do!), now you know exactly what to look for and you will catch it much sooner, while the plant can still be saved by leaves or cuttings or whatever.
As I suggested before, you just have to be consistent about a few things (soil, light, water) and Echeverias can have long and prosperous lives. Usually with colorful hummingbird magnets for flowers.
The Echeverias Database
