Can a person really die quickly from biting their tongue?
I know of an ER doctor who had a patient who removed (by biting and pulling) every last part of her tongue, she survived that (although, her ability to speak was probably shot). The stump of her tongue clotted before she could even go into shock (at least where it was really serious). 

Here is a quote from the book Angels in the ER  (this is a paramedic speaking with the doc):


  "Every bit of it. Gone. And the funny thing, Doc, is it didn't even
  bleed very much."
  The doctor then asked his patient to open her
  mouth... "it was gone!"



It would certainly be possible to commit suicide doing this if one was a hemophiliac or continued to remove the clot from the hole(s) in their tongue (although the latter could be a potentially painful and I have a feeling that it would take a very, very long time!).