If you've ever walked into an Ashtanga Yoga class, I'm sure you've noticed that it's warm in the room, but not even close to as hot as Bikram. The warmth helps your muscles to loosen up slightly, but the quick-paced and strength building vinyasas between poses is what really heats up your body. Think of it as creating an inner fire that heats your body from the inside out, which helps you loosen up tight muscles. It also makes you sweat a lot, which helps in detoxification.
Drinking water during the practice prevents that heat and puts that internal fire out. Not only that, but if you stop every 10 minutes to take a sip of water, you interrupt your breathing and the flow of the sequence, which in turn will disrupt the moving meditation you've got going on.
It is very important to drink 10-12 glasses of water throughout the day so that you are well hydrated by the time you arrive at class. If you've been drinking all day, you shouldn't need to drink during class, however, if you are feeling nauseous, overheated, or dizzy - definitely listen to your body and drink water if necessary.
Fit's Tips: Depending on the class you go to, some Ashtanga Yoga instructors are very strict about this, which I personally don't agree with. As an instructor myself, I trust that my students are better able to make decisions about their own bodies. If an instructor you take class from makes you feel uncomfortable about your need for water (or anything else for that matter), talk to them after class about it. I'm sure they'd want to know how you feel.