I can add a member to 'GroupX' like this:

$member->addToGroupByCode('GroupX');

How can I remove a member from 'GroupX'?

According to 'cms/code/MemberTableField.php':

$member = DataObject::get_by_id('Member', $memberID);
$member->Groups()->remove($groupID);

Thanks! How can I remove the $groupID for the group named "GroupX"?

I *think* you are able to put a where clause in the relationship getter...

$member->Groups("Name='groupname'")->remove($groupID);

swaiba, your code still uses $groupID but I don't know the $groupID.

$doGroup = DataObject::get_one('Group',"Name='GroupX'");
$member->Groups()->remove($doGroup->ID);