Except there is no rule which provides for an umpire to call a batter out for throwing the bat, unless the bat actually interferes in a play. Some rule sets allow for a restriction to the bench after a warning but none have an out ruling just for throwing the bat.
We had it called this summer. One of our girls all of the sudden started throwing her bat. She was warned in her first AB for hitting the catcher with the bat and then in her 2nd AB was called out. It was a big call at the time because she hit a double on the play and we were in the middle of a rally. 2 outs at the time so it ended the inning