To mean business is to be serious about what one is promising or proposing to do, but the speaker is indicating that they let people know that are joking by biting back
Consider the statement "I bite back, not enough to do damage but definitely enough to let him know that I am joking and not at all serious about what I am saying.". Based on this "I bite back, not hard enough to do damage but definitely hard enough to let him know that I mean business." a true statement? Yes, no, or I don't know?