Can I remove "friends" and still have them be in my mafia?

Yes, you can remove friends after you've joined their mafia or they have joined yours.

Once someone is in your mafia, you can delete them from your friends list and they will still be in your mafia. You will still be able to send them gifts, energy packs and promote them to Top Mafia, however you won't be able to help them on jobs and vice versa.