Will my coaches football workout make my body cut?

Haha, I would say so! Any regular exercise will help to tone and this seems more than adequate. If you eat everything in moderation, focus on getting plenty of protein, and replace your typical beverages with water you're guarenteed to see some changes to your build. By "cut" I assume you mean something a little more than just a little toning... So if you don't see drastic enough changes after 2 weeks or so then add some more muscle-building exercises to your regiment. Just don't forget to eat right and drink lots of water everyday!