This is kind of a rude question. Many vets are willing to negotiate to some degree, but if you walk in saying "I need my cat spayed for free and if you kill her I will sue you" then the answer is always going to be no. If you find a rescue that has space or that helps people get their cays spayed, and that rescue has a relationship with the vet and a reputation of payment, and the rescue vouches for YOU as a person: that you OR THEY will commit to truly care for this cat for the rest of his/her life and not throw her away the first moment she pees on the carpet because something hurt and she cat't get to the litterbox on time, or scratches the furniture because you have not explained to her where in the territory the residents may sharpen their claws and get those itchy jagged edges off, etc, then many vets will do as much as they can afford to do to help you, recognizing that the lights must be kept on and staff paid, etc....
I don't know of any reputable vet that does spay/neutering for free. Try Googling low cost spay clinics.
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