I accidentally made a couple of extra saves when I was clicking through the menu to save. I'd like to delete the extra save files, but I can't find the save file location anywhere and I haven't noticed a delete save option in game. Does anyone know where the files are located? I'm on Windows 10 and playing through the GOG launcher if that makes a difference.

There is no actual save file, Dex save game data are values in Windows registry located in HKEY_CURRENT_USER\Software\Dreadlocks Ltd\Dex.
Registry values can be deleted, but I suggest you to be cautious: you might want to make a backup before altering it.