Clip art used to be clipped from one medium and stuck to another as part of layout design. This clipart caught on quick and spread faster than a Greek army inside the walls of Troy. Free clipart became the new epidemic, infecting designers high and low with its accessibility, utility, and quirkiness.
Don't have a friend or relative draw or design it for you. Just because someone is artistically inclined or has a good eye for design, doesn't put them in the same category as a professional cartoonist. Cartooning is a very specialized field - a talent that is honed over many years of trial, error and experimentation. You may have an idea of what you want, but executing it on paper is harder than most people think. It takes a professional.
One effective option schools turn to is clipart, but beware - there is a lot of poor quality clipart. One important factor to consider is if the clipart image you find comes in a set with matching graphics. It is best to use the clipart from a source that specializes in school mascots, so you can get your mascot in a variety of poses. Using the exact same image each time gets tiresome. Being able to inject some variation, without losing consistency-of-style, is important. Look for clipart sets that feature your mascot doing a variety of things suitable for yearbook, banners, posters, t-shirts and other school related activities.