Hi

A long time ago I was trying to install quakespasm for quake. When that didnt work I downloaded many different sourceports for the game (they also didnt work). The thing is that they are still in the game directory. Is it possible to wipe the game and install it completely new without the old files or do I have to remove every sourceport manually?

Sure.

Yes, you can.

I think I have downloaded some games like 4-5 times as the computers or their hard drives broke; several games both Windows and Linux versions. Despite that I do try to avoid unecessary downloads.

You have two questions here.
1) perfectly possible to download the quake installer files as much as you want from you gog account.
2) system maintenance. You can uninstall a game (or app), but you may need to uninstall mods separately. Look at start menu, uninstall each of they have items there. If they are just mods, most likely they do not install, so uninstall the game, and check the folder in install is deleted. Also check documents, and user folder - type “%appdata” in explorer window without quotes. You may have registry entries left, hopefully be ok.

Once clean install game from downloaded or saved installers. Note, always install games outside windows folders like program files, it’s cleaner. And only install what you need, removing anything you don’t. Makes keeping system cleaner easier.

In terms of removing the source ports, you'd probably want to use a bulk uninstall program if those source ports did anything with the registry or installed anything to other directories.

Just deleting the folder would likely be sufficient to just get the game installed in a vanilla manner though, if you don't mind registry entries or remaining files elsewhere.