No, you cannot actually remove someone from your "Friend of" list. LiveJournal gives users complete control over whom they list as friends. Allowing users to remove people from their "Friend of" lists would give them control over someone else's choice of friends. Also, there would be no way to prevent the user in question from simply adding you to their Friends list again.
However, if you are uncomfortable with a certain username displaying on your "Friend of" list, it is possible to hide that particular name by banning that user from leaving comments in your journal (http://www.livejournal.com/support/faqbrowse.bml?faqid=20). This will automatically prevent their username from appearing in your "Friend of" list. You may also hide the name of a community in your "Member of" list by banning it from leaving comments in the same manner.
If you do not wish to ban the user in question, or if you would prefer that other users would not be able to view your "Friend of" list at all, you can choose to hide the entire list so that it does not display to other users when they are viewing your User Info page (http://www.livejournal.com/support/faqbrowse.bml?faqid=61). Hiding this list also hides your "Member of" list. You can't, however, hide your Friends list or the list of communities to which you have posting access, since you are always able to remove someone from your Friends list (http://www.livejournal.com/support/faqbrowse.bml?faqid=61) or leave a community at any time (http://www.livejournal.com/support/faqbrowse.bml?faqid=82). Also, you will still see your own "Friend of" and "Member of" lists when you view your User Info page while logged in.
However, please keep in mind that hiding who lists you as a friend by following one of the methods above does not make that information entirely inaccessible. For example, users with paid accounts can still use the Directory (http://www.livejournal.com/support/faqbrowse.bml?faqid=123) to retrieve this information. Additionally, certain off-site tools may also have access to it.
If you do not want your entries read by a particular user, you should make your entries either Friends Only or Private (http://www.livejournal.com/support/faqbrowse.bml?faqid=24). Public entries are viewable by anyone, whether they are viewing the entries through their Friends page or by visiting your journal directly. Similarly, when someone adds you to their Friends list, they do not gain access to your Friends Only or Private entries. However, you will see all of your own entries on their Friends page while you are logged in. This is simply because you always have access to view your own entries. See http://www.livejournal.com/support/faqbrowse.bml?faqid=35 for more information.