Actually, from an evolutionary perspective, it makes a LOT of sense for Andalites to be able to throw up. It would probably happen through the hooves, just because it tends to be easiest for food to go out the same way it came in.
See, throwing up is nature's way of expelling toxins from the body. You eat something you weren't supposed to eat, and suddenly you dun feel s'good. And, next thing you know, that thing you weren't supposed to eat is no longer, um, eaten.
And think for a second about how Andalites eat. Granted, I figure, given that they eat off the ground constantly and almost never actually stop and look at the things they eat (they eat as they run, they don't have the time to stop and analyze every blade of grass to make sure it isn't actually some kind of poisonous plant), they probably would need to have a MUCH more robust digestive system than most terrestrial animals. It would probably take a lot to kill an Andalite.
. . . Which, now that I think about it, explains SO MUCH about Ax's eating habits in human morph.
But, still. Every creature has SOMETHING that is toxic to it. And, in evolutionary terms, plants actually don't like to be eaten, and will generally evolve exactly those toxins that will keep things from eating them. So, Andalites would need a way to expel from their bodies those few things that have managed to become poisonous to them. Thus, they would have to be able to, um 'toss their cookies/tango with the toilet/technicolor yawn' as Marco might put it.