Make the Sandbox Mesh bigger than the non-rectangular Surface.
Switch View > Hidden Geometry > ON.
Select the outline of the Surface [not its face] and use Edit > Copy.
Now Edit the Grouped Mesh.
Use Edit > Paste-in-Place
The Surface’s outline should now overlay the Mesh’s geometry.
It should also automatically cut the Mesh.
Erase the unwanted parts of the Mesh so its outline matches that of the Surface…
You don’t need to use a sandbox grid to use the sandbox tools to modify the grid. If you create a grid with another tool, e.g. Curviloft (Fredo6), Extrusion tools (TIG), Artisan (Whaat), …, you can use the tools too.
Is the non-rectangular surface:
a) - planar or or not,
and
b) - do you wish to replace an existing non-orthogonal mesh on the (sur-)face by the rectangular grid created by say the sandbox tool?
When editing the mesh group, before pasting the outline in place, convert all the lines of the mesh to Soft, Smooth. Then switch to wireframe mode and hide all lines. Turn “View Hidden Geometry” OFF. The mesh will now show as an unbroken face. Now paste the outline in place. It will cut the face, and you can easily delete the portions of the mesh outside the outline.