Sorry your dentist is being so unsympathetic!
Your reaction is your gag reflex, which is automatic, but it can be controlled.
What you need to do is to practice.
Sit or lie with your mouth as wide open as you can. Wait a few seconds, and then breathe deeply and slowly through your mouth and nose. This will prevent your gag reflex from starting, with a little practice.
When you get to your dentist, explain that you have an over-active gag reflex, and you would like him to stop working and remove his instruments, and the suction tube from your mouth when you raise your hand, which you will do if you feel your reflex coming on.
The knowledge that you have control, together with this technique, will mean that eventually you will be relaxed enough to let him work away.
If he won't co-operate, or pooh-poohs your request, find another dentist!