First, as Meleeguy said, it is a figment, and figments CANNOT cause damage.
Second, whatever the action is, a surprise round is 1 STANDARD action only. Which means the image can move, or it can break the staff. It cannot do both.
Third, it sounds like you are trying to find loopholes in the system to make an uber-powerful character for yourself. Good luck with that. If I was your DM, I'd give the opponent a +10 to Will save just for the absurdity of a high level character breaking a Staff of Magi to get rid of an insignificant kobold ("OMG! Elminster just broke a Staff of the Magi on little ole level 1 Commoner me! I am so gonna believe that...!!!"). For a low-mid level intelligent monster who has never even HEARD of a Staff of the Magi, let alone its effects, I'd give an even bigger save bonus. Assuming that the figment can do damage, of course, which it can't.