Building on @Mark_Bailey suggestion, you can have JMP generate a Tabulate for you that matches the existing graph without writing any code or manually duplicate any settings. Here are the steps:
1) Build your graph in Graph Builder;
2) Launch the Hover Label Editor from the Hover Label RMB menu:
3) Select a Tabulate Preset from the Graphlets panel (selected by default):
4) On the "Filters" tab, set Skip Filters to 1 to remove all filters (the default is to filter down to just the data under the current visual element).
Now hover over any element in the graph and you will get a thumbnail of the corresponding Tabulate window as a thumbnail inside the hover label.
Click on it to launch a fully functioning Tabulate on its own window.
Below is an example for a Tabulate built from a bar chart with two nested variables on X (which will map to your Tabulate rows) and two response variables, one for Y and one for color (which will map to the Tabulate columns).
Note: Another option is to skip step 4, launch the filtered down Tabulate, and then remove the Local Data Filter to get a Tabulate for the entire data table.