The answer is "it depends". It depends on the country and it probably even varies between universities.
In some countries, Sweden or the Netherlands, for example, it is virtually impossible to force a graduate student to leave, though eventually the funding allocated to that student may expire. I am aware of one case of academic misconduct in the Netherlands where the student was more or less forced to quit or otherwise face a long and painful series of disciplinary hearings to officially make him leave.
In other places, Belgium, for example, students are often paid based on year long contracts (graduate students are employees). The contracts can be evaluated each year and terminated in the case of unsatisfactory performance. Of course, matters are handled delicately, and often by involving the student in the process. That is, discuss the student's performance and paint a bleak picture and let him/her see that quitting is the best option.
From the student's perspective, it is best that they do not waste 4+ years of their lives and achieve nothing.
From the university/department/professor's perspective, it is best that the student does not waste 4+ years of funding and achieve nothing.
It's a win-win.