The Chinese sentence is playing with the multiple meanings of the word "聪明". In “xx學生不是不聰明，就是不好好學” (It's not that the student XX is not 聪明, only that he didn't take time to study.), "聪明" means having high IQ (intelligence quotient), as that could be determined by the rigorous psychological test. In the sentence "不知道時間的寶貴、學生時代學習機會的難得而只是貪玩，這是最大的不聰明" (It's the biggest non-聪明 to not know the value of time and the opportunity of study as a student, and to play all the time.), "聪明" means wise or 明智. In both cases, you could use the English word "smart" just like "聪明" in Chinese. But if you think about it, the exact meaning of the word in either English or Chinese is different.
Playing tricks with words sometimes can impress people and give others thought-provoking ideas that sound clever, smart or 聪明. But those words should be taken as nothing more than clever talk.