This line of "reasoning" is fallacious because the attack is directed at the person making the claim and not the claim itself. The truth value of a claim is independent of the person making the claim. After all, no matter how morally repugnant a person might be, he or she can still make true claims.
For example:
Witness: "I saw X murder the shopkeeper."
Defense attorney: "Isn't it true that you are a convicted felon?"
On the other hand, illuminating real character flaws and inconsistencies in the position of an opponent are a vital part of the public political process and of the adversarial judicial process.
Use of a personal attack in a logical argument constitutes a logical fallacy called Ad hominem, a term that comes from a Latin phrase meaning "toward the man".