Can I e-file my federal taxes and file my California State taxes by mail? How do I e-file federal without auto e-filing state? Hoping to save the $59 for state e-file.

Yes, you can.  But there is not a fee for e-filing.   The fee you pay is for the tax preparation software, so it applies whether you file electronically or by mail.   

Ok thank you! I recall filing my state taxes for free last year on Turbo Tax and my situation has not changed - do you know if there is a way to file your state tax for free even if you have to pay for Deluxe for your federal taxes?

To file your state return for free you could try going to the state's tax site.    But if you used a paid version of TT for federal there is no way to use TT to do the state for free.

https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/contact-state-department-revenue/L9qVToi02_US_en_US?uid=m6e06um0