You are correct. In fact, she SHOULD have written "have" rather than "of". "Might of" is not casual English : it is a basic error and - most worryingly - is evidence of the writer's ignorance of basic grammar. You might want to consider finding someone else to learn from. Someone who cannot write correct English has no right to be charging money for English lessons.

"Might have" is correct. When spoken aloud, "Might have" sounds like "might've." "Might of" is completely incorrect, but, when spoken aloud, also sounds like "might've." There's only the smallest difference, maybe no difference at all. People who didn't pay attention in school and know the language mostly by speaking it may actually believe the phrase is "might of." This can find its way into writing. I wouldn't necessarily reject the tutor. The mind works in strange ways and I constantly find my fingers typing elementary blunders, when I know better. I can think "they're" and type "their." I can imagine thinking "might have" and typing "might of." If this is a "community tutor" and not a "professional teacher," you may have found someone who speaks authentic, informal, colloquial English. Depending on your goals, that might be fine; conversational practice, for example. I feel that I am paying a community tutor for the trouble of making and keeping appointments, for a session that is 100% in my target language rather than 50/50, for someone who will be patient with me, and--above all--someone who really will stop and correct every single mistake I make. I see that italki has nine hundred community tutors in English, but only about half of them claim to speak "advanced" English.

Might have is correct. When spoken, it changes from [might have] to [might'av] to [might'uv]. Since "of" is pronounced [uv], some native speakers incorrectly write "might of" [might'uv]. If you have had a satisfactory experience with the tutor, by all means continue. However, it is very likely that most other native-speaker tutors will be better at basic grammar and writing.

You are correct, Bing. I agree with Paul and Su.Ki. You should find a more qualified tutor.

My advice, do not take a lesson with this tutor. You're right, it's wrong. Nobody who is being paid to teach English should ever make that mistake.