Hagrid was expelled in his third year at Hogwarts due to being blamed for the death of Myrtle (who became Moaning Myrtle). In the first two books he lives on the grounds as the Keeper of Keys and Grounds at Hogwarts, he can't be banned.

Rubeus Hagrid was expelled from Hogwarts in his third year (1943) and was subsequently banned from practicing magic. He was wrongfully accused by Tom Riddle of opening the Chamber of Secrets and releasing a monster (his pet Acromantula, Aragog) that supposedly killed a student, Myrtle Warren (Moaning Myrtle). Because of the seriousness of the accusation, the Ministry of Magic snapped his wand in half. However, Albus Dumbledore, who believed in Hagrid's innocence, persuaded the Headmaster to allow him to stay on as the Assistant Gamekeeper. For the rest of his life, Hagrid technically operated under this ban, though he famously hid the pieces of his broken wand inside a pink umbrella to perform simple spells. It wasn't until 1993, after Harry Potter proved Hagrid's innocence by defeating the true monster of the Chamber, that his name was cleared, though he never formally returned to finish his magical education.