I'm a student who has been playing the clarinet for about 3 years now. Within that span, I never used a mouthpiece patch until my music teacher recommended it, and I also bite quite hard on my mouthpiece. I recently got a mouthpiece patch and am attempting to relax my embouchure, but I fear it may be too late as there have been bite marks on my mouthpiece for a while now. Do bite marks really affect the playing of my instrument? Should I get a new mouthpiece?
I played clarinet for a year and bass clarinet from Grades 6-12 in school concert bands, and I never had bite marks on any of my mouthpieces. I therefore can't really answer your first question, but I can answer your second--get a new mouthpiece and finish learning how to relax your embouchure fast.
I typically tighten my lips when playing clarinets of any kind. I don't tend to bite down that hard.
The root problem here is: "you are doing it wrong" , i.e. your embouchure is incorrect. While it is true that people may generate very small marks or even tiny indentations where their upper teeth hit the mouthpiece, major divots are a strong indicator of incorrect mouth pressure.
It will be long and painful to re-teach yourself, but you've got to train your mouth to apply much less "clamping" pressure and more uniform pressure from all sides. I'll note in passing that the much-adored Buddy Wright (principal, BSO for 40 yrs or so) used a double-lip embouchure. You might try that for a while to help train your jaw to reduce bite-strength.