Do you want to perform this kind of analysis with SAS instead of using the JoinPoint software??? Or do you just want to produce this kind of graph with SAS after you have calculated the data points? This might be a question for Tech Support -- I would expect you'd have to know how the math behind the JoinPoint software compares to the math of the several SAS regression procedure techniques.
You might want to look at a post I made to SAS-L a couple of years ago. In that post, I addressed fitting a segmented regression model. I only presented mechanics for fitting a model with a single join point and I did not show any of the permutation distribution testing. But that post might provide you with some basic methods which you can extend as necessary.