The usage is correct, but it's unclear which part you are calling into question.
At the top-level we are using the word "can" (which is a modal verb, aka modal auxiliary) in a typical fashion: "I am eating cake" -> "I can eat cake" is analogous to "I am having it mailed to you" -> "I can have it mailed to you."
Within the sentence "I am having it mailed to you" there is a structure whose name I don't know. Compare with "I am letting him speak to you" and "I am watching you speak to her."
EDIT: The sentence "I am having it mailed to you" gets its structure from the fact that "have" is a causative verb. It would seem that "let" is a causative verb but "watch" is not. I am trying to see what we might call "watch" in the above context.
EDIT 2: The verb "watch" is a verb of perception.