How long can a cut extender tendon on the back of the thumb go with out treatment. ?

How severe: If you truly cut your extensor tendon, and in affects your ability to extend your thumb, then it comes down to whether or not you want to ever regain use of that ability. Deep /gapping lacerations should almost always be sutured, ideally within 12-24hrs. Tendon lacerations most certainly need to be sutured, and if more severe - surgically repaired asap. Get seen asap!