Crash when saving

Are you shutting down all non-essential programs before starting the game, especially anti-virus and any backup programs that may be monitoring the My Documents folder?
For example, a few people have had BitDefender block the game from being able to create files and folders, which has caused issues when saving, though usually errors rather than crashing. In those cases, including both the game executables and Larian Studios My Documents folder in BitDefender's trusted app and directory sections would fix the problem (Advance Threat Defense, Ransomware Protection / Safe Files, Application Access).
Windows Defender has also caused issues; in that case an exception for the game can be made in Start, Settings, Updates & Security, Windows Security, Virus & threat protection, Virus & threat protection settings, Add or remove exclusions.

Try browsing to the '..\Documents\Larian Studios\Divinity Original Sin 2 Definitive Edition\LevelCache' folder and delete the contents. A corrupt file there can cause problems when saving or loading.

Try exiting out of the Steam client, if applicable, and starting the game directly from the '..\SteamApps\common\Divinity Original Sin 2\DefEd\bin\EoCApp.exe' program file, by right clicking and running as administrator.

If you create a new profile and start a new game, can you save properly?

If applicable, disable Steam cloud support either globally (in the client click on the Steam menu and select Settings, and then Cloud) or just for this game (in the library right click Divinity: Original Sin 2 and select Properties, then switch to the Updates tab and check the Steam Cloud section).
Alternately, exit out of the Steam client, or Galaxy for GOG, and just start the game directly from the executable when required.

Next, try browsing to the '..\Documents\Larian Studios' folder and rename the 'Divinity Original Sin 2 Definitive Edition' 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. With Steam / Galaxy running and cloud support enabled, the client would just download the cloud copy of your existing profile.
After that, start D:OS 2 DE, create a new profile and see if you can start a new game and save/load. If that works, exit and then copy a couple saves from the renamed folder into the newly created profile's ..\Savegames\Story folder. If that lets you load the saves and re-save, move the rest of the saves over.
If the game still crashes, delete the new My Documents D:OS 2 DE folder and rename the original back again.

If a new game in a new profile also crashes when saving:

Try creating a new Windows administrator user account (either with the My Documents folder in the default location, or on a different drive, if available), switch to that account and try starting the game from there, directly from the executable.

Try doing a clean boot and then test the game. Click Start, or hit WinKey-R, type in msconfig and hit enter; in the General tab, click Selective Startup, uncheck Load startup items (if required) and leave Load system services and Use original boot configuration options checked. Next, click on the Services tab, check the box to Hide all Microsoft services, then click the Disable All button (maybe make a note of which are currently enabled/disabled), then click OK and reboot the computer.
Run msconfig again to switch back to the normal boot configuration.

If a new game is fine but recent saves crash, please reply with your latest save (or a Dropbox or Google drive link, etc); if older saves are ok, reply with the most recent save that you can load and re-save, and the oldest that crashes. If you are using any non-Larian mods, also include a list of those enabled and/or the modsettings.lsx file from your profile folder.
Each save is a folder in the '..\Documents\Larian Studios\Divinity Original Sin 2 Definitive Edition\PlayerProfiles\<ProfileName>\Savegames\Story' folder.
In Windows Explorer you can zip a file or folder by right clicking on it/them and selecting 'Send To | Compressed (zipped) Folder'.