What is the term for a sarcastic statement directed at a person that includes an element of insult?

The term that best describes a sarcastic statement directed at a person which also includes an element of insult is sarcasm. Sarcasm involves saying the opposite of what one truly means, often in a sharp or cutting manner, with the intent to ridicule or express contempt. This aligns closely with the definition given, where the statement carries an insulting undertone directed specifically at an individual.

While irony refers to a broader concept where the intended meaning is different from the literal meaning, and it doesn't necessarily have the personal element of insult that sarcasm does. Mockery is a form of derision or mockery directed at someone but can involve more than just sarcasm. Satire is a literary genre or technique used to expose and criticize foolishness or corruption in individuals or society, but it is not typically aimed at an individual in a personal way like sarcasm. Therefore, sarcasm is the most fitting term for the definition provided.