If I've understood your post, your DC was sent out of the classroom for "whispering". As s/he left, the teacher said that your DC was a "waste of space and oxygen". I'm not sure how loudly this was said?
Your DC has told you that this expression made them feel like the teacher effectively said they might as well kill themselves ....
If your DC has MH problems and you have previously been worried about his/her wellbeing, I might be concerned. Otherwise, I would view the teachers comment as unprofessional but not really harmful.
I'd wonder why my DC wasn't more resillient because the reaction doesn't fit the expression.
But, you're reaction that it would make you feel worthless etc. is really interesting. It is fair enough to be pissed off by what the teacher said, but it isn't the sort of phrase that would cause most people distress as such.
Perhaps its would be worth taking stock of whether you are hypersenstive and have instilled this in your DC?
Its certainly not in the same league as calling a child a thick cretin!!!