If you use the "selection" tool (under the tools menu or the fat plus symbol on your tool bar) you can select just the graph. You can also click on the graph title to edit (or delete).
Hello nlc4. We have a one-page guide describing how to save out graphics from JMP using the technique that karen@boulderstats has outlined. It is available on our learning library: jmp.com/learn or directly here: http://www.jmp.com/academic/pdf/learning/01_publication_quality_graphics_windows.pdf
You can also see how to do it in this quick video I captured here: