When someone repeats something that you said, but tries to change the meaning, you can say that that person is "twisting your words around".
For example, imagine that you told your little sister that she could borrow your laptop. You said this:
You can have it after I'm done with it.
Now she says that you promised to give it to her permanently. She says:
You told me that I can have it. That means it's mine now.
You might respond like this:
You're twisting my words around. You know that I just meant that you could borrow it!