in my humble opinion, there is nearly never a reason to save a graph as you have described. in nearly every case it causes unnecessary problems. Either the graph is easy to disassociate from the data or the data is duplicated. Both will generally end badly.
Please consider clicking on the red triangle menu at the very top left and Save the Script to the Data Table.
This keeps the graph script with the data and, obviously does not duplicate the data.
JMP Systems Engineer, Health and Life Sciences (Pharma)