I find this phrasing a bit surprising, but maybe I can learn something about words here.
I've only ever heard "degree" used as an intangible noun, to refer to the achievement or title or whatever you want to call it.
Is it common to use it to refer to a physical object? Is it an informal way of saying diploma? Maybe a British way of saying diploma? I made some brief checks of online dictionaries and couldn't find that usage.
A 'diploma' to me is a 'degree-equivalent' (as determined by government; not, perhaps, by employers) qualification offered by non-universities.
As you said, you can't sieze someone's degree, at best you can invalidate it.