CiviMail allows you to exclude recipients of a previous mailing. I think this is what you need.
Lets say you are sending to the Newsletter Subscribers group:
1) Send your First mailing of the week out as normal
2) When you are ready to send the Second mailing, choose the same newsletter group as last time, but choose to exclude recipients of the First mailing.
In your case, it sounds like you want to send out a message to an arbitrary 50% (now I understand why you asked the question!) or so of the first group. Unfortunately, there is no limit to 50% button. One approach would be to create another group based on Newsletter subscribers that contains ~50% of your initial group and use this for the first mailing. Another approach might be to do an Advanced Search with the criteria a) Newsletter recipients b) some other criteria that splits the group in half (a smart group for users with an odd contact ID, maybe?!) and then choose the action Email - schedule/send via CiviMail.
Whichever method you choose, once the first email has been sent, you can use the approach mentioned above to send the second email.