Link is able to hit the Octoballoon before it blows up, but doing so is rather pointless, as it will blow itself up momentarily. Furthermore, Link can defeat the mini-octoroks left behind, but since they disappear in just a matter of seconds, there isn't much purpose in doing so. These mini-octoroks will do a 1/2 heart of damage if they come into contact with Link.
Palace of the Four Sword
In the Game Boy Advance remake of A Link to the Past a second Octoballoon can be found within the Palace of the Four Sword. This variation has an orange color, but serves a nearly identical function as the standard red Octoballoon . It won't leave quite as many smaller mini-octoroks when defeated. This Octoballoon is surrounded by more dangerous Orange Octoroks.
Octoballoon Sprite and Shadow from A Link to the Past.