How do I clean a saxophone mouthpiece?
The whole job takes two minutes. Take off the reed and ligature, run the mouthpiece under warm (not hot) water with a drop of mild soap, work a mouthpiece brush through it (the small tapered brush made exactly for this), rinse, dry with a paper towel. Done. Weekly is plenty for a student. Hot water is the one real hazard: it warps the material, and a warped mouthpiece plays wrong forever.
If build-up has gotten ahead of you, a short soak in equal parts white vinegar and water loosens it. No bleach, nothing abrasive, and never the dishwasher.
We also sell mint mouthpiece sprays, a quick alcohol-based cleaner that keeps things fresh between real cleanings. Students actually use them, which counts for a lot.
And since this question is usually really a question about renting: every mouthpiece that comes back to us is cleaned and sanitized before it goes anywhere near the next player, and the sax it belongs to gets checked over and re-kitted at the same time. Ask us what happens to an instrument between renters sometime. We are happy to walk you through it, because we are proud of it.