Can I resend an email to new people from the same campaign?

Yes.

When you sent the email to the original recipients, they were marked with a Campaign Member status of "Sent" in the Campaign.  If then add new people to the Campaign as Campaign Members, add them with the Campaign Member status of "Targeted".  Then, just hit the Send button in the Campaign, and it will only send the message to those Campaign Member with the status of "Targeted".

You can also resend the email to everyone in the Campaign; however, note that this will create some data confusion on the Campaign Member data.