The original name of ISU's teams was the Cardinals. After a game which ISU won resoundingly, the next day's newspaper printed a headline on the other team being hit by an "Iowa Cyclone", or something to that effect. Have provided a reference link:

Actually, Iowa State had no nickname before one sports reporter said they rolled through a team like a violent cyclone. Before that they were the Iowa college of Agriculture. The cardinal (Cy not psy) was added do to the high number of cardinals on ISU's campus. Which is 10 miles from were I live. Report It

Because the school's offical color is Cardinal. It is easier to have a mascot of a bird than a tornado.

Because Psy, the bird's name, is a bird that is like a cyclone at the bottom.