i feed my goats alfalfa hay quite often, they seem to like it, I don't see why it would bother them to be in a field of it.
As far as clearing it I wouldn't know any other way except using a chemical of some sort.

Why do you want to kill off the alfalfa? It is perfectly aceptable in a pasture for goats. Most hayfields already contain grasses that can be used for grazing. If the field is getting thin, or you want to increase the amount of more palatable pasture grass, you can do frost seeding next March

Heavy grazing will naturally reduce the amount of alfalfa in the field over a couple of years.

Here is a link that might be useful: OMAFRA Goat Pasture Seeding Recommendations

Sharon,
I want to kill the alfalpha because I am planning on putting horses in the pastures as well as goats, and from all I've heard, alfalpha is too rich for them. Otherwise I'd rather leave well enough alone.
Thanks!

How rich in alfalfa is your pasture? If it isn't a relatively recently seeded hayfield, I would be surprised if it was too rich for your horses. (I know they pick the plants they eat, and many horses will head straight for the alfalfa candy if given a choice.) Wait to see how much remains after a season of grazing by the goats. Letting them graze it through September will weaken the alfalfa more than the grass.

Even if a field contains a lot of alfalfa, you can manage their grazing by giving the dry hay early in the morning before letting them on the alfalfa pasture. One more year of horses and goats on the pasture and there won't be much alfalfa left.