I'm not sure what part of the novel you are currently reading, but at the beginning of Speak, the reader finds out that the school's mascot was originally the Trojans. "Officials decided that it needed to be changed because of the word's connection to a well-known condom brand. When the mascot is changed to the Hornets, the students start making up questionable cheers about the "horny" hornets, and so it is changed again.
The constantly changing mascots seem to represent not only the changes that Melinda experiences throughout each quarter of the school year but also the school's focus on insignificant school elements. While Melinda endures bullying and struggles to decide on what she should do about the summer's events, school officials worry more about the mascot and Melinda's surface issues (attendance) than the academic and emotional well-being of their students. This tendency to "major on the minors" is truly common in the real academic world and is often satirized by modern writers.
In regards to mascots' connection to high school culture, for most students the mascot represents school unity and pride. Because Melinda refers to the mascot changes in a nonchalant manner throughout the novel, she demonstrates even more that she is an outsider to the school--she simply does not identify with the school or the students and teachers who make up the school's body. The students who are most concerned with the mascot changes are those who play sports, who are popular, and who belong to the school's elite cliques.