The beer mug is not "refillable" in the sense that the soda mug is. The mug costs $10 and holds 22 oz. of beer. When you get it filled, you pay for the standard 16 oz. beer, so you get an extra 6 oz. of beer each time. You can get it at most of the bars on board. Actually, they'll probably push it on you if you order a beer on the first day of the cruise.
I did the math once, and I think it worked out that if you buy 10 domestic beers or 8 "premium" beers, then the mug pays for itself. The downside is that it's made of glass and is pretty heavy, and lugging around the ship all the time is kind of a pain. It also doesn't fit in the cup holders in the seats of the Walt Disney Theatre. We bought them on our first cruise, but haven't bothered since.