Translation:Why do today what you can get others to do tomorrow?
The infinitive 'gjøre' is used here, I believe, in a manner similar to English, which is shown in the translation 'Why do today'. In English the meaning of this is 'Why should I do today' or something like this. As you can see, both the subject 'I' and the conjugated modal verb 'should' have been removed. If I am correct this explains why it is 'hvorfor gjøre' and not 'hvorfor gjør'
It's part of a set expression, it's there in English as well. Å få noen til å gjøre noe. To get someone to do something.
But in a conversation you could skip "å gjøre" in the part after the comma, as mostly everyone would understand it is just suppressed (it is a part of the argument set in the first part). I would not skip it in writing though.
I disagree with grydolva in that the word 'til' is in the English translation of Å få noen til å gjøre noe (To get someone to do something), because a literal back translation of this is Å få noen å gjøre noe. Not being Norwegian I agree with grydolva that it is a set expression and that 'til' is required. If you think of older English then words like 'til' make a little more sense, though they can still be difficult to remember. Using some old English patterns the sentence used translates to Wherefor do today what one can get others for to do tomorrow. The bottom line is though we need to learn when words like 'til' need to be placed in sentences. Which is something I'm still trying to understand myself.