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Derpy the Mailman is a mailman that delivers mail to the Mushroom Kingdom. It's possible that he is based off of Derpy Hooves from My Little Pony: Friendship Is Magic. In SuperMarioGlitchy4's videos, he appeared in some in his bloopers, with the newer bloopers having a less appearance of Derpy.
Derpy the mailman's color code is gray all over, except on the hair which is blond. This look is then similar to Derpy Hooves's.
He also has derpy eyes, hence his name.
Derpy the mailman appeared in the 8th skit of the blooper "Ssenmodnar 2 (100th video)", saying "DERP" in the corridor which leads to the courtyard in Princess Peach's Castle. He made a cameo appearance in the "Adventures of mario & luigi ep 1", where Derpy shoots an envelope at Mario, who is hit with the mail. Mario then reads it only to be hit by another envelope that Derpy also shot.