In almost all cases, there is no way to remove a councillor except when periodic elections come up. Then it is up to the electorate.
One answer is to use the facilities provided by most email systems to block or divert emails from someone who is agreed to be a troublemaker. (If the email system doesn't support this, get a better one).
In the past I have been involved in doing this, where a councillor was deemed to be harassing the clerk. Their emails were diverted to a couple of supportive councillors. The clerk did not see them. Any genuinely important issue was handled by the councillors, with the clerk's involvement if appropriate.
If there are no councillors willing to take this role, then the emails could simply be rejected and the councillor in question told that they can only contact the clerk in writing. That would almost certainly at least slow them down.
I'm afraid there is no complete answer to difficult councillors.