Yes, just like when you want to buy an item of $50 with a $100 bill, the seller would return a change of $50 back to you, but they know at that moment that you have $50 in your pocket. Coin control is important for privacy reasons and you should use it to select UTXO's that you want to spend. Or you can send the UTXO through a mixer and receive in it in new and unused address before making the payment you want to make.
Warning is using mixer means your bitcoin will likely be marked as tainted coins by exchanges and centralized platforms. It can trigger their bots to mark your accounts on their platforms as suspicious and your accounts can break their Terms of Service, AML policy. Your account even can be frozen, terminated by AML violation and you have to think carefully before deciding to use a mixer.
If you don't want to have issue and you don't need too high privacy, you don't actually need to use mixers.