I tried installing a mod for the Witcher 3, but I gave up trying to put it in the right place; I removed every content of the mod so there is no trace of it.

When I launch Witcher 3 now, it is a black screen when I try to launch.

I recently just got it today.

Before you say, yes everything is up to date, graphics drivers are up to date. I was able to play earlier, but decided to exit to figure out how to get the console, but you had to install a mod for it.
When I launch the game, I cannot exit out. I have to CTRL + ALT + DEL and sign out.
Bump. I need help.

I tried uninstalling and reinstalling Galaxy, but no prevail.

I tried launching it without Galaxy; wouldn't work.

Honestly, it sounds like your install of the mod corrupted something important. I'd go ahead do the following:

1) Copy your saved games into a temporary folder somewhere like on your desktop
2) Uninstall Witcher 3
2a) If you know what you're doing, regedit and ensure that HKLM\Software\Wow6432Node\GOG.com\Games is clear. If that didn't make sense to you, DO NOT TRY TO DO THIS STEP
3) Download and re-install Witcher 3
4) Copy your saved games back into the saved games directory

That will take a little while, but it sounds like your best bet is a clean install, sadly. If you re-download the game through Galaxy, you may want to select the "archive" option (or is it called backup? I don't use Galaxy and forgot) so that you have a copy of the installer files handy, just in case something happens again.

Yep,as OneFiercePuppy said reinstall and don't try to remove files again
or you will have the same problem again.

Have you asked Galaxy to verify the integrity of the game?
When my DEFCON licence was revoked I just got Galaxy to verify the game and it worked.

Open Galaxy > Click the game in the left hand box > More > Manage > Verify/Repair