In the world of 'Harry Potter', Hagrid is considered a half-giant, half-wizard. His magical abilities were questioned when he was expelled from Hogwarts in his third year on erroneous accusations of opening the Chamber of Secrets, which led to his wand being snapped.
However, he concealed the pieces of his wand in his umbrella, which suggests he retained some magical abilities post-expulsion. But truly, Hagrid is more than any label - he's a friend, teacher, and protector.