You cannot stir (or ladle from) a pot of soup on the blech, and so must serve it only when removed from the blech.
As to returning it to the blech, this is permissible, provided that all the following conditions are met:
- You intended, when you removed it, to return it.
- You've held it the entire time it was off the blech. (It can sit on a table (but not the floor), provided you're also holding it.)
- The food is fully cooked.
- The food, when you return it, has not cooled completely.
In cases of necessity, either of those first two conditions (not both) suffices along with the latter two; in cases of great necessity, the latter two conditions suffice alone.
Source: Sh'miras Shabas K'hilchasah, chapter 1, paragraphs 17–20 and 31–32.