This is yet another awesome search term. I believe the answer is yes, a PI can indeed kick out a graduate student. For many reasons, but I’d say the main one is due to irresponsibility on the part of the student (or a very sick (mentally speaking) PI). I have yet to see this happen, but there are urban legends about this issue. Remember, when you join a lab you sign a contract with the university and/or department and/or PI. I can’t exactly recall who “owned” me while I was in grad school, but basically I was to become a member of my department and work under the wing of my former PI. One very, very important detail to remember is that when you decide to join a lab/group you’ll more than likely have a conversation with the PI regarding project(s) to take, lab policies and expectations (and vacation time, don’t forget that). One such thing to discuss is working hours (whether 9-5, or 6 or 7 or 10pm), how often to be in the lab or office (depending on your discipline) and even how often to meet with the PI to give progress reports. Because your relationship with your PI is contractual, if one of the parts fails to deliver, the other can feel free to sever ties with the failing part.
In my current lab there’s a student who has been there for a number of years. That student hasn’t made significant progress (in their own words) on the thesis project and a few weeks ago started working like a maniac, as apparently the PI was fed up with not getting publishable results. The student said that there was a risk of getting kicked out of the lab, and thus why the sudden peak in performance and delivery of results. Whether it was a real possibility or just an “incentive” to get the student’s hands moving, it has worked. But also, this situation presents the very real consequences of one of the parts not delivering the way they were supposed to. So, yes, PI’s, if they reach a critical point, can kick a student (or lab tech, postdoc, or other lab members) out of a lab.