How do I permanently remove cookies?

You must first follow the basic steps , take cursor on top menu bar > click on history and clear all history & website data .

Then click on go > to go folder and type ~/Library find a folder cookies - delete all contents to the trash , restart the Mac and empty the trash .

Open safari , and its preferences > click on general new window opens with > change from top sites to home page and also for new tabs open with as homepage , so that if you set this setting the home page will be your web browser ( can be safari , chrome ) .

If you want cookies never to be saved in your system use private browsing : Safari for Mac: Use Private Browsing windows in Safari

For setting private browsing permanently as shown in the screen shot set safari opens with new private window .

Go to Finder and select your user/home folder. With that Finder window as the front window, either select Finder/View/Show View options or go command - J. When the View options opens, check ’Show Library Folder’. That should make your user library folder visible in your user/home folder. Select Library/Cookies. See if deleting the files there helps.

Cookies and other website data will be populated from sources other than the obvious open pages and tabs. They include Top Sites, Quick Website Searches, Search Engine Suggestions, Top Hits, Subscribed / Shared links and feeds and others. You need to investigate all of them.