This joke only works with an American accent. In fact, it took me a moment or two to work it out. In standard British English, 'tutor' is pronounced 'tyoota', so the pun doesn't work. You have to use the American pronunciation (known as 'yod-dropping') to get the homophone tutor/tooter.
That said, when it comes to farts, we in Britain have an even better joke. One term for 'a sudden blast of malodorous hot air from one's behind' is .... you guessed it.... 'trump'. Hee hee.