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Shocking new footage shows Florida State quarterback De'Andre Johnson PUNCHING a woman in the face HARD at a bar in Tallahassee ... after she punched him in the face first.

It all went down at the Yianni's nightclub on June 24th ... after the woman felt Johnson was aggressively trying to push his way past her to get to the bar.

In the video, released by the State Attorney's office, you can see the woman -- a 21-year-old FSU student -- raises her fist to warn Johnson and he grabs her hand. She then punches him in the face with her left fist.

That's when 19-year-old Johnson responds by throwing a crushing right cross to her face ... you can see the woman bleeding all over the bar.

The woman says she suffered a black eye, swelling all over her face and a cut on her nose.