How do I take my daughter's "legal" father off of her birth certificate since we're getting divorced and he is not the biological father?

First of all, being a parent and being on the birth certificate doesn't require that the father be the actual biological father.  If he has assumed the role of father and has been in the child's life, you cannot simply and unilaterally take him off the birth certificate.

You would need to most likely go to court to change this and he would need to be notified to protect his due process rights.  If he refuses to take his name off of the birth certificate, you may not be able to take it off either.  Unfortunately, the court is not going to be looking at your concerns in terms of his rights to her unless there is an issue of abuse.  The court will be looking at the child's needs and rights to support first.  If your soon to be ex-husband desires visitation, then the court will also look to those needs, as well.