No - there isn't. The drink of the day glass is just a souvenir that doesn't have any discounts associated with it. Save the space in your luggage!
**Technically** the beer tokens aren't supposed to carry over between cruises, but that has never been enforced. I was talking to someone onboard back in January and they said they had heard from a CM that the beer token was going to be added to the Navigator app at some point and the physical token phased out. I've carried a token for years (already have 3 mugs) and that would be a bummer for sure.