Start a petition. If you don't like your school's mascot, your friends and fellow students probably don't either. Write up a brief petition to the school board stating why you object to the current mascot and ask that the school board support your request to change it. Collect as many signatures as you can -- students, faculty and parents.
Present your petition at a school board meeting.
Enlist a parent to speak on your behalf. Suggest that the school board appoint a committee of students and faculty to create a list of possible new mascots with drawings of what the new "official" team logo would look like. The students can then vote on which new mascot they prefer.
Hold an election. Make ballots that include the names and drawings of the new mascot candidates and have the students vote. The mascot with the most votes wins.