There are various slang words for 'woman' or 'girl' in common use these days, but mort isn't one of them. The OED says the word is now historical and archaic, and that formerly it was often accompanied by a distinguishing word - the Dictionary has gentry mort, kinchin mort, strolling mort, walking mort and autem mort. A kinchin mort was a little girl; in the 16th century tramps used the term to refer to girls of their own community. Boys were kinchin coves. Kinchin probably relates to a Germanic word meaning 'child' (cf the modern German Kindchen, little child). Strolling usually referred to an itinerant and was often used disparagingly, as was walking mort, a wandering vagrant woman. Autem is an old cant word for a church (in his A Dictionary of the Underworld, Partridge notes that earlier slang dictionaries claimed that autem came from the Yiddish a'thoumme, meaning a forbidden church), and an autem mort was a married woman.
The OED says that the etymology of mort is unknown, but it may be from Romani, or an alteration of the French amourette, flirtation.