How to remove the anesthetic for teeth in as fast as possible?

You cannot: Your body will metabolize this out of your system at its own rate. It is not your choice.

Oraverse: Oraverse is an anesthetic reversal agent that can be injected to shorten the half life and effects of local anesthetics used in dentistry.

No need to do so..: I am sure your dentist is already using short-acting, and smallest amount of anesthetic needed for particular procedure. Thus, there is no need to remove (and you can't once injected)--because the anesthetic will disappear quite fast on its own without problem. So, if you don't want it to linger too long, work with your dentist to use only short-acting form. Good luck.

Remove tooth local: Yes there are reversal drugs for local anesthetics in trials. Phento-lamine mesylate is one that counter-acts the blood vessel constricting effect of the small amount of adrenaline in local anesthetics. Dr. Stan malamed at usc has done extensive research in local anesthetics. Google his work for more info. But then talk to your dds/dmd about shorter acting local anesthetics.They can help.