Can I suspend my mercenary?

Yes, you can suspend and unsuspend your mercenary using the Mercenary UI window. While suspended the mercenary does not show in group and does not require upkeep. After suspending your mercenary there is a 5 minute delay before you can unsuspend them, and you will be charged an upkeep fee as well.

You cannot suspend or unsuspend your mercenary while you or one of your group members is "in combat." If you will need your mercenary for a particular fight make sure you unsuspend them before you start the fight.

To save money you probably want to suspend your mercenary whenever you won't be needing them for a while.