There is no direct way to do this with MIXED. This is a nontrivial matter, and there are lots of things to consider. There is a nice procedure called GLMSELECT for linear model selection, but only for fixed effects. A fascinating macro has been written to do what you are asking. See:
http://www2.sas.com/proceedings/forum2007/191-2007.pdf
for a description. I have not used it, and it looks like it takes a lot of effort to set up and get to run (initially). But the output, including graphics, look great.