Biological sex is a simplification based on statistical averages for the sake of easy classification. That may have its uses in some educational contexts where the focus is not on that subject, but that simplification is not a valid rigorous definition.

And if it IS determined by only one characteristic, then it is equal to that characteristic. If the one chosen is, say, chromosomes (which are also not a binary characteristic), then other factors like reproduction, hormones, etc., are not determined by biological sex.