You must NOT stop giving your son formula. Until 1 year, formula or breastmilk should be the primary source of nutrition. Cow's milk has too much sodium and potassium for his kidneys to handle at this age, is hard on his stomach and can cause anemia. It simply doesn't have the proper balance of nutrients for an infant, so in rare cases stopping formula before 1 year can even cause brain damage.
It's also not necessary to introduce juice at all, ever. I have never given my child juice -- she drinks water and eats fruit, which is much healthier (juice is very high in sugar relative to the vitamins in it and it lacks the dietary fiber of fruit. I'd given juice watered down with at least 50% water if my child refused fruit or needed it for constipation, but otherwise I'm not giving it).
It's possible to give formula through a sippy cup, although generally that's not done until more like 10 months. I don't imagine a 6 month old would be able to take the necessary 24-30ish ounces of formula through a sippy. It's normal for a baby to go through a biting stage as they learn how to suck with their new teeth. I say just buy some more nipples and wait it out. You could also stop the feeding and set him down when he bites the nipple (just like a breastfeeding mother would do when she is bitten) and then resume it a few minutes later to try to teach him not to bite.