Please email supportdos@larian.com, with a description of the problem and the report.zip file generated by the
D:OS support tool (for the PC version). The report will contain system and game information, any crash dumps, and your saved games (assuming they were at least partially written).
Try starting the game directly from the '..\SteamApps\common\Divinity - Original Sin\Shipping\EoCApp.exe' program file, by right clicking and running as administrator. If you start a new game can you save then?
Are you shutting down all non-essential programs (especially anti-virus) before starting the game?