Tenant gave notice to vacate and decided to stay. I offered 9 month renew option but did not sign lease yet (neither has she). She has begun to make unreasonable demands and I have decided I would rather sell than deal with this type of scenario. Can I give her proper notice that I plan to withdraw the lease offer? Is that legal if I haven't signed the lease agreement?

Yes, it's legal. Give her a written notice that you have withdrawn the renewal option, her tenancy is terminated and she has 30 or 60 days to move out. The time for the notice depends on what was in the previous lease and the laws in your state.