Here are 3:
It could be literal, meaning somebody was physically thrown from something. Imagine someone throwing another person off a boat and into the water!
It also means to tell someone to leave, so it's similar to 'threw me out', but it needs to be something that uses 'on/off' and not 'in/out'. An example could be, "His performance on the stage was so bad that they threw him off (the stage)." In this case, they told him to leave the stage.
Another use of 'threw me off' is to lead someone to believe something false or confuse someone. Imagine this: you think a friend is planning a surprise birthday party for you. Then they tell you they're going on holiday and won't be there for your birthday, so you stop thinking they are planning a surprise party. But then they DO have a party for you and you are very surprised. You could say, "I knew you were planning a party, but then when you said you were going away you threw me off!"
Perhaps this last one, meaning to confuse or mislead, is the one you wanted.