Is there a process to tidy the tables created by logging?
Writing "code" could be as simple as a cron script that runs daily and does mysql -u user -ppassword -e "DELETE FROM log_civicrm_group WHERE log_date &lt; DATE_SUB(NOW(), INTERVAL 2 MONTH)" databasename, which deletes records older than 2 months.

EDIT: To address your comment, if you want to completely disable logging but just for this table, you could drop the associated triggers. This might get turned back on during an upgrade if there's a change to the trigger, but can deal with that then.
e.g.

SHOW TRIGGERS LIKE '%civicrm_group%';
DROP TRIGGER civicrm_group_after_insert;
DROP TRIGGER ...

Repeat and replace civicrm_group_after_insert with the various triggers.