Q: Is there such thing as flossing too often or with too much pressure? Sometimes I have that hard to get piece of meat and floss until it comes out and causes bleeding.

A: You can actually cut your gum while flossing.  In the situation you are asking about, it is difficult to tell if the bleeding was caused by the meat, aggressive flossing, or some other gum/periodontal involvement.  If you notice bleeding while flossing daily, you should consider getting a periodontal evaluation by a dentist.