Are you shutting down all non-essential programs (especially anti-virus) before starting the game? Firewalls have caused conflicts (generally on loading screens, or during the save/load process) and and update to either program or the game could start causing a conflict.
If you check the Event Viewer, does that give an error code or 'Faulting Module' file name that might help identify the cause of the crash?
- click Start (or WinKey-R or WinKey-W in Win 8), then type "event viewer" into the search box. in Windows 10, 'event' should bring up 'View event logs'.
- after starting the Event Viewer, expand 'Windows Logs' in the left column and select 'Application'
- in the center column, look for a recent error (maybe sort by Date and Time) for the game
- check the information under the 'General' tab below the list of events, starting with "Faulting application name..."
Try browsing to the '..\Documents\Larian Studios' folder and rename the 'Divinity Original Sin 2' subfolder.
This folder contains the saved games, configuration files and a level cache folder. Deleting or renaming it will get the game to recreate it on startup; playing the game from a different Windows user account would effectively do the same thing.
After that, start D:OS 2, create a new profile and see if you can start a new game and save without crashing. If that works, exit and copy a couple saves from the renamed folder into the newly created profile's savegames folder. If that lets you load the saves and resave, move the rest of the saves over.
If a new profile doesn't help, delete the new My Documents D:OS 2 folder and rename the original back again.