Performance issues

Do you have similar problems if you start the Classic version of the game? (assuming this happens early in a new game, so is feasible to test)
For example, there is a known driver issue which could cause low performance in the Definitive Edition (often on the order of 10 FPS), but Classic was fine, which should be fixed with the latest nvidia drivers (hotfix link). Often this could be fixed by disabling the 'Hardware-accelerated GPU scheduling' option in the drivers; with at least the Windows 10 May 2020 update, and nvidia 451.48+ drivers, or Adrenalin 20.5.1 Beta for AMD, you should also be able to disable this in Windows (click the Start menu and select Settings, then in System, Display section, on the right side select 'Graphics settings' to get to this option).

Are you shutting down all non-essential programs before starting the game, especially anti-virus, graphics utilities, or DirectX injectors, etc?

Try lowering the graphics settings and resolution, or switching to Windowed or Fake Fullscreen display mode, to see if that makes a difference.

Try lowering the sound quality in-game. You could also try changing the Windows sound quality settings (one person with D:OS EE reported that a very high default sound quality caused performance issues in-game).

Try verifying local files: in the Steam library, right click on the game and select Properties, switch to the Local Files tab and then click on the 'Verify Integrity of Game Files...' button.
With the GOG version, in the (optional) Galaxy client, select the game, then the settings icon at the top right (beside the Play button) and under Manage Installation select 'Verify / Repair'.

Try exiting out of the Steam client, 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 (or '..\Divinity Original Sin 2\Classic\EoCApp.exe' for the original release).

Try right clicking the executable, select Properties, switch to the Compatibility tab and check off the 'Override high DPI scaling behavior' option (set it to Application), run as administrator and disable fullscreen optimization, and set a Win 7 or 8 compatibility mode, to see if that makes a difference.

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, extract the replacement folder from this download into your '..\Documents\Larian Studios' folder, and see if you have any performance problems in a new game (start on Story difficulty and skip through as much as possible of the starting section to get to Fort Joy).

The graphicSettings.lsx file is set to 1280x720 Windowed mode, Very Low quality preset and low audio quality, which you can change in the options (manually, or hit autodetect) if this helps.
If performance in a new game is back to normal, create a new profile, exit and copy a couple saves from the renamed folder into the newly created profile's ..\Savegames\Story folder. If that continues have good performance after loading your recent saves, try increasing the graphics settings, and if you don't run into any serious issues, move the rest of the saves over.
If the game still has performance problems, delete the replacement My Documents D:OS 2 DE folder and rename the original back again.

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.

Try creating a new Windows administrator user account, switch to that account and try starting the game from there, directly from the executable. If you can not test in a new game (if Fort Joy is fine, for example, and the issue started after getting to the next map region), you would need to copy your latest save over from your current account's My Documents folder to test.
Each save is a folder in the '..\Documents\Larian Studios\Divinity Original Sin 2 Definitive Edition\PlayerProfiles\<ProfileName>\Savegames\Story' folder.

Try resetting your graphics driver's 3D settings to default (right click an open area of the desktop to start the nvidia Control Panel or AMD Radeon Settings).

If you check the graphics options in-game, is the nvidia / AMD card listed, rather than integrated graphics, if applicable?

If you recently moved your desktop computer or changed monitors, etc, make sure the monitor is connected to the discrete graphics.
The connector for the integrated graphics would be (usually) vertical with a desktop computer, near the rear USB connectors, ethernet port and audio jacks; the connector for an nvidia or AMD GPU would (usually) be horizontal, below the motherboard's group of ports, on a slot by itself (probably with exhaust vents).

Make sure the Virtual Memory setting in Windows is set to automatic / system managed, rather than being disabled or set to a fixed size. To check or change virtual memory settings, see the applicable guide for Win 7/8 or Win 10.

Make sure DEP (Data Execution Prevention) is set to default, or exclude the game:
1) open the Start menu
2) for Win 7
- right click 'Computer' and select 'Properties'
- click 'Advanced system settings'
- select the 'Advanced' tab and click the 'Settings' button in the 'Performance' section

for Win 8 or 10
- right click 'This PC' and select 'Properties'
- click 'Advanced system settings'

3) select the 'Data Execution Prevention' tab, and if applicable:
A) change the DEP setting to the first option (Turn on DEP for essential Windows programs and services only)
B) leave it set to all programs, and add an exception by clicking the Add... button and browsing to the '..\Divinity Original Sin 2\DefEd\bin\EoCApp.exe' program file
4) confirm by clicking the OK button, and reboot if any changes were made

One person with performance issues with D:OS EE on an i7 CPU fixed it by setting the game not to use the first 2 CPU cores, since Windows was running everything else on them, as well. Another was getting stuttering, and fixed it by switching the game to use only one core, applying, then switching it back to all 4 cores.
To try this, start the game, then start the Task Manager (Ctrl-Shift-Esc or right click an open area of the Task Bar), switch to the Processes tab, right click on EoCapp.exe and select 'Set Affinity...'. After that, try unselecting Core 0 and 1, apply and test the game, or unselect most of the cores, apply and select all of them again.

Also in the Task Manager Processes tab, try right clicking EoCApp.exe and under Set Priority, select High or Realtime.

If that doesn't help, please contact support with a dxdiag report (WinKey-R, type in dxdiag and hit enter, then when it finishes loading click on the 'Save All Information...' button and save the report somewhere handy). Also check the '..\Divinity Original Sin 2\DefEd\bin' folder for the gold.log file to include (if it is more than zero bytes).