You will need the Profile Deactivate permission to perform this action. When a profile is marked as deceased, they will be archived and will not appear on communication related reports such as address labels, giving statement greetings, etc.
To mark a person as deceased, navigate to their profile and then go to Actions > Archive in the upper right.
Then in the pop up, choose "Deceased" as the reason. You will also be shown a list of any involvement they had.