I am looking for something similar to sc_game truncate, but to remove preceding moves (from a current position), rather than remaining ones. Does such a function exist in the API exposed to scripts called via tcscid.exe?
The SCID tool's focus is on collections of positions more than single games.
Accordingly, the best way to do what you're trying to do is to deal with the PGN directly. PGN is flat text and available in SCID.
If you want part of a game, the typical action is to copy the PGN into a text document from SCID, and edit the part that you wish. Load your edited game back into SCID if you want ..