What should I do if advisor asks me to move to another university or lab for strange reasons?
There are many plausible reasons why the professor may not want to reveal what exactly you said was inappropriate; most likely the professor doesn't want to inadvertently reveal the identity of the person who accused you of inappropriate behavior in order to avoid retaliation or further confrontations.

As a grad student, you are considered an adult and a professional. What matters here is not whether you intended to cause harm, but whether your behavior caused harm. As we grow up the world tends to become less forgiving of our mistakes, and the professor has every right to remove someone from their group to maintain a healthy working environment. Although it is also possible that whatever offensive thing you said was simply the last straw that broke the camel's back, so to speak. Either way, you should reflect on your behavior and tendencies and learn from the mistake. If there are mitigating factors (e.g., being a foreign student, mental health problems, etc.), ask the professor nicely to reconsider... but don't expect anything. Ultimately a successful grad school career depends to a large degree your relationship with your advisor. If the relationship is so broken that your professor is trying to kick you out without any prior warnings (I assume), then there is no point in forcing the matter, no matter how famous the professor is.

Also some assumptions in your question is unwarranted... Why do you think the professor has planted "spies" among the students? More likely the professor learned of the matter because someone reported you. I think you over-estimate how much the professors care about the everyday activity of their students.