Yes, looking at a persons details in MindMyMinistry (while logged in as an administrator), you'll see a Reset link at the top right of your screen.

Using this option will erase the person's login details completely so that they can complete the signup process again and get a new password.  This is most often used when someone has changed their email address and wants to sign up to MindMyMinistry using their new email.

Afterwards, remember to invite the person by clicking the Send Invite button.