...is? Is this possible? I have a mixed dog I bought from a farm and I'm sure it's part Beagle, but no one knows what breeds the mother is, nor do they even know what the father was. I'm just interested to know for breed characteristics.

Nope, the DNA test is for purebred dogs. They put a dogs DNA on file and that way if there's ever any question about parentage they can test the offspring and compare it to the parents.