How to make my iPhone untraceable?

There is no way to make any cell phone untraceable. Your carrier always knows where your mobile phone is. That’s why criminals buy “burner” phones or get stolen phones that they use for only a few days, then discard. And even they can be tracked, although it is harder and thus used in only major criminal investigations.

Well, you do know that your carrier knows exactly where you are at all times, correct? If you don't want them to know where your phone might be, you will have to turn off the phone.