The title and the loan are independent of each other. But, no, you do not pay taxes again to remove a co-signer or to refinance.
Do I have to start over if I refinance my car?
Refinancing does start your auto loan over. When you refinance a car loan, you choose a new loan that has a different rate and possibly a different term. The new loan replaces your current loan. Refinance terms offered by lenders most commonly are from two to seven years.
Does Refinancing start your payments over?
Refinancing doesn't reset the repayment term of your loan, but it does replace your current loan with a new loan. You may be able to choose from different offers for your new loan depending on your goals, including a longer or shorter repayment term.