What is "Tao of Jeet Kune Do" known as in Cantonese?
Bruce Lee was trying to create an original 'school' of martial art style of his own.


  What do Cantonese-speakers refer to it as?


We consider the 道 in 截拳道 (Jeet Kune Do) is the same ones in 跆拳道 (Tae Kwon Do) and 柔道(Judo). 

道 in 截拳道 actually represents 'school of martial art style'. It has very little real connection with the other 道 (Tao /the way) - a school of Chinese philosophical thinking 


截拳 - intercept fist 


'fist' represents 'strikes/ movements'  in martial art


道 - School of martial art style
之道 - philosophy of 


"截拳道之道" [zit6 kyun4 dou6 zi1 dou6] literally means "The way (philosophy) of movements interception style martial art" 

Actually the concept of 截拳(intercept movements) was not an original concept Bruce Lee invented. It was very much borrowed from the 詠春拳 (Wing Chun style martial art) he had studied under the famous Wing Chun grandmaster 葉問 Yip Man in his youth.