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TMZ Sports has obtained the 911 call made by the fiancee of Cleveland Browns offensive line coach Andy Moeller ... in which she claims he strangled and beat her ... and it wasn't the first time it happened.

During the call, the woman is clearly distraught and out of breath -- and in the process of fleeing Andy's house, where she had been staying while visiting from Maryland.

She tells the operator, "[Andy] just tried to strangle and beat me. I'm leaving the premises and I gotta get out of here quickly."

During the call, the woman says the two were engaged -- "Not anymore though."

As for what triggered the incident, the woman claims she was talking to her son on the phone when Moeller told her to "shut up" ... and then got violent.

"I kept telling him to stop and not to hurt me."

As we previously reported, cops responded to the scene -- but didn't see any evidence of an injury. Hours later, the woman told officials she no longer wanted to press charges against Moeller.