I think what the other commenter was trying to say was not that it would be impossible to do so, but that it would not be "right", so to speak.
While you could of course exile them like other countries have done in the past, why would you do that? What reasoning would you use to justify exiling them, striping them of their personal property etc. ?
Abolishing the monarchy is one thing, it can be justified pretty easily, the interests of the people. Anything beyond that however would be punishment, what have they done that is currently illegal that warrants that punishment? Punishing them simply "because they are royals" doesn't really work out, that isn't illegal after all.
Technically just abolishing the monarchy / taking away their powers would suffice.