does Nutro have any discounts or coupons to save on there brand?

Frequently you can get coupons from the company's website by signing up for their newsletter. I've received coupons from several companies (Earthborn, Merrick and The Honest Kitchen) that way and they continue to email me ones periodically.

Nutro sends reps out to the big chain pet stores on the weekends to promote their products. They always have coupons. Contact the stores in your area and ask if they have one.