How would I cut across a plane using a die-like mesh/curve? I'm in the process of creating a visual model of a product made using 2D CAD software. The .svg which I have imported into blender is the file sent to a laser cutter which would out cut across an acrylic sheet wherever there is a path in order to form the shape.

I was wondering if there is a way of cutting the plane such that the result would be similar to what would be carried out by the laser cutter (imagine the resultant shape being cut out of plane using a knife with runs along the path, if that makes sense)

I've tried to use the Boolean modifier to achieve the effect I am looking for but with limited success. It only seems to cut out a small section of the design for reasons which I do not understand:
To cut the shape on the plane with a curve object you can use Knife Project tool. Place your curve object above the plane, while its selected hold Shift and select the plane, switch to Top View, then Orthogonal View by hitting 5 on the Numeric Keypad and change to Edit Mode.  

Then In Edit Mode select Knife Project in Tools tab.

To avoid errors in the mesh, before using Knife Project tool you can subdivide the plane few times or convert the curve object to mesh.