Who is the biological mother of Gon?
Unfortunately, this question cannot be answered right now.

When Gon was younger, Mito told him that both of his parents were dead. However, it is later found out that it was a lie, because his father Ging was obviously alive and well.

Before the Greed Island Arc, Gon got a tape from Ging. At the end of the tape, when Ging was going to tell him about his mother, instead of listening to it to the end, Gon just stopped the tape and stated that Mito was his mother.

There is a lot of speculation as to whom his mother could be, but until Togashi supplies the answer, we will never know.