This is what someone asked me the other day. Actually, we do have punctuation when we speak - in a way.
The basic unit of spoken punctuation is the pause. Where we would insert a comma in written English, we insert a tiny pause when we speak:
When I reached home, I made a cup of tea.
Where, in written English, we would add a full stop, we add a slightly longer pause when speaking.
In a formal situation, such as a speech or presentation, we add an even longer pause as a 'paragraph break' or to signify the beginning of a new point.
Interestingly, there is not a good way to signify inverted commas in spoken English, which has given rise to the air quote:
Another interesting crossover from written to spoken punctuation is when people say 'period' out loud to punctuate a particularly strong point, one which is the last word on the matter.
I don't care what she said to you. It's wrong to hit girls, period!