When you invite people to your SignUp using a direct invitation from SignUp.com, they are sent an invitation link that is coded to their unique email address. To later block a person from accessing your SignUp, delete their contact from the SignUp's Participants tab (click the x in the right column next to their name). Doing so will invalidate their personal link to the SignUp and delete their assignments.
If people you delete from the Participant's list try to use their link in the future, they will get a "Whoops!" notice letting them know they are not a Participant on the SignUp.
Note: if you invited people using a Shareable SignUp invitation, then the person can re-enter using the same or different email address. When privacy is imperative, please invite people using direct invitations only.