"I think the tutor is late again."
Translation:Dw i'n meddwl bod y tiwtor yn hwyr eto!
The bod is the verb "to be", so it's literally something like "I think the tutor's being late again" (with possessive "tutor's being", bod y tiwtor).
You can't leave off the bod since it's the "being" in that sentence. (Or if you turn it into the more natural in English "I think the tutor is late again", it's the "is".)
"the tutor's being late again" acts sort of like the grammatical object of "think".
English doesn't do it like that, but it's a little bit similar to the object raising with "want": I want the tutor to be late -- where "the tutor" is grammatically the object of "want", though meaning-wise (semantically), it's the subject of "be late" -- and German, for example, would have to say it that way, as the equivalent of "I want that the tutor is late".
There, too, you can't leave off the "to be" from "I want the tutor to be late", because it doesn't correspond to the "that" alone, but to the "that ... is" (I want that the tutor is late) in the changed construction.