If I purchase my own insurance, will Rover still deduct it?

I am not exactly sure what you mean. However, if you are referring to the percentage Rover takes from your bookings, no, that will not change one cent if you purchase your own pet-sitting insurance. Rover's cut covers their guarantee and backup support, among other things. So it is not strictly "for insurance." In fact, Rover does not even provide "insurance." Instead it has something it calls a guarantee. It would probably be a good idea for you to read about Rover's guarantee and what it specifically covers. This Help page provides various links to that information:

https://support.rover.com/hc/en-us/arti…

FYI, your own pet-sitters insurance would be deductible for tax purposes, as a business expense.