Please, don't - I'm not

The usual form of such conversations is

Do not X

followed by

I am not X-ing.

This is because in the first line, one refers to not doing the action of X in general, while in the second, one refers to not doing X in that particular situation.

"I am not" means "what I am doing now is not." Example:

Alice: "Please don't drink and drive"

Bob: "Oh, I don't" (Bob never drinks and drives)

Ellen: "Please don't drink and drive"

Frank: "Oh, I'm not" (Frank is not currently driving while drunk. [He could be currently drinking but stating his intention not to drive home])

It has to do with the difference between these two present tenses. "I'm not mocking you" is clearer as it refers only to what is taking place at the moment when it is said. "I don't mock you" is a little ambiguous, as it could mean that the speaker never mocks the other person. I think that the alteration does improve it as it removes this ambiguity.

I'm not a native english speaker, but If I say "Do not mock me" to someone, it implies that I'm thinking that one is mocking me, or going to mock me. So I think the answer might be "I'm not" or also "I won't", depending on the context.

PS: Answering with "I don't mock people" also sounds right to me.