No one wants to be disrespected and deal with a smart-mouth. People who communicate with sarcastic, snide or biting remarks can make interactions uncomfortable. Some of these people are trying to push your buttons, as is often the case with adults. Some may be unaware of appropriate interactions and must be taught, as is frequently the case with children and adolescents. Either way, utilize tactics to defuse and resolve harsh situations and learn to deal with and perhaps even heal a smart-mouth.
Maintain an even temperament. The worst thing to do in response to smart-mouths is to reciprocate the behavior and show they have gotten under your skin. If you are dealing with a kid, show your level of maturity by not shooting back words in response or in anger, especially when interacting with your own child. If you are dealing with adults, make sure they see they have not antagonized you.
Appear to ignore the comments. Whether dealing with adults or children, you can defuse their efforts by continuing the conversation as if you were not addressed in such a sarcastic way. For example, if your comment of, "I really need to work out today," is met with, "Why bother? You didn't work out yesterday either," you could respond with, "Yeah I know. It's really tough getting behind on working out."
Talk to the person after the moment has passed. Make sure you and the other person are calm. Convey that the smart-mouthed behavior hurt you and you found it inappropriate and rude. Be prepared for the feedback to be negative or even defensive. Don't bite. Continue to stay calm and focused.
Remove yourself from interacting with smart-mouthed people. Simply don't talk to them. This act demonstrates to these people that there are consequences for their behavior, and it does so without shouting or aggressive threatening. Tell them you won't be engaging in conversation unless they come to the table with respect for you. When you deal with children, give them concrete examples of how to communicate respectfully.