How do kill my Bermuda grass that is mix up in my st Augustine ?

Pull out Bermuda by its roots. Wet. Ground slightly as that makes pulling easier. It's usually pretty easy to do by pulling up runners to find main roots. Do small section at a time if u need. After piling out Bermuda, fertilize St Ausgustine so it fills back in quickly.

Bermuda has a deep root system that won't stay pulled out. It is a more durable grass than St. Augustine, and you may have to accept a mix of St. Augustine with Bermuda.

Your best bet is to make sure the St. Augustine stays healthy. Set your mower to its highest setting. You will still need to mow regularly, but St. Augustine grows better when allowed to get a bit taller. If you currently have your mower set low then you are helping the Bermuda which accepts the shorter mowing height better. Water regularly, especially during dry periods, as St. Augustine needs consistent moisture. Bermuda is drought tolerant, so forgetting to water helps the Bermuda to out compete St. Augustine. If, however, you experience a long wet and warm period your lawn could be hit with brown patch or gray leaf fungus. Treat the lawn with the proper fungicide if you notice either of these. If your St. Augustine grass turns yellow or dies in patches it is probably caused by chinch bugs. Keep an eye out for disease and insect problems. Begin fertilizing St. Augustine about 3 weeks after it greens up in the spring with a 3-1-2 ratio slow-release fertilizer (15-5-10 or 21-7-14, etc.). Repeat fertilizer every 10 weeks through summer. You may need to use a fertilizer with iron if your St. Augustine is pale or yellowish. Stop fertilizing 4 to 6 weeks before the first expected frost date.

Mindshift’s answer is probably the best. You could use glyphosate if you don’ t mind small dead patches in your lawn. You would have to protect your other grass when you use it. I’ve used a bottle with a small opening as a guard to spray or paint the poison on a small spot. Cut the big end off and hold bottle opening very close or on the Bermuda while you spray.