Every month our branches get a list of people that have been charged off by the bank due to NSF or some other reason. If one of these customers comes into a branch and wants to cash an on-us check can we collect the money owed us from that check? Do we refuse to cash it unless he pays us what do you suggest?

This is best asked of counsel familiar with your setoff laws. Personally, I believe you have the right to do business or not with anyone. But the person who may be most upset here is your customer on whose account the check is drawn. How do you tell them you won't cash their check because this person is a deadbeat, without violating privacy laws and getting sued. Even if you just remained mum, the depositor with good funds may get upset.

If the funds are deposited, clearly you have the setoff opportunity. Otherwise, you may find that negotiating with the customer then and there (with the check in your hand) is the way to get some recovery on the spot and make arrangements.

Off the top of my head and without any research, I'd be slow to advise excercising setoff in your scenario. The right of setoff arises from mutual debts. In this case you have a customer with an account. That is a debt owed by the bank to the customer. Payee who comes in with the on-us check is presenting the bank with a direction from customer to pay the payee. Payee has a debt to the bank but I am not sure the direction to pay creates a debt between the bank and the payee. Without that mutuality of obligations there is no right of setoff.
Also, why get a good customer angry at you just to collect from the deadbeat? Probably end up with two former customers.