[Robert B. Mercer]

I did not come by way (I did not arrive riding on top of) a turnip truck (a farm truck carrying lots of the vegetables, turnips),

or, what I always hear:

I didn't just fall off of a turnip truck...

It means:
I am not stupid... I am not stupid like a child... you think I know nothing, but I am smart... you are trying to pretend you are smarter than me, but you are not....

Why?
People in the city (sometimes) think people who live on farms are stupid. So, the sentence is saying:
"I did not come from a farm, riding here on top of a truck carrying vegetables like a stupid person."


Other phrases like this:

I wasn't born yesterday!
I'm not as dumb as I look!
I'm not as stupid as I look!
I didn't just get off the boat! (I did not just arrive here)

Or, you can ask the question:

Did you just fall off the turnip truck? (Are you as stupid as a farmer?)
Did you just get here by boat? (Are you new here and stupid?)
Are you as dumb (stupid) as you look?