Is there any mechanism through which NATO member states can agree to remove a member state? If so, then what are the criteria through which a member state could be removed?
When the North Atlantic Treaty was signed first in 1949, no provision was included for removing a member state. Therefore I guess that there would be no legal pretense for removing a member state as long as this member state follows the duties included in the treaty.
However, any member country has the right to withdraw from NATO at any time. Therefore, if all but one country would have come to a common understanding, they could theoretically all withdraw at the same time and recreate a very similar treaty, effectively being equivalent to removing a member.
There is nothing in the North Atlantic Treaty that mentions suspension or expulsion from NATO.
In absence of this, I look at the Vienna Convention on the Law of Treaties. I look in particular at Article 60, which covers the termination or suspension of a treaty in the event of its breach. In this case, all other parties would need to be unanimous in their decision to either suspend or expel the country that defaulted on its obligations. Any NATO member (apart from the country whose expulsion is being considered) would be able to veto such an expulsion.