Yes, it can
The only limitations on a controlled mount are “... It moves as you direct it, and it has only three action options ...”. It’s bonus action and reaction (and legendary and lair actions) are not limited so it can use them to do whatever it could normally use them for, like taking opportunity attacks. As the mount is an NPC under the control of the DM (usually, it is possible for a mount to be another PC), they ultimately decide what the mount does.