3D Printing

If you can get state boundary image data coincident with height map data (such as by taking two screenshots on the USGS website, one with the heightmap data opaque and with it translucent, without panning or zooming between), you could use a normal image editor (eg: GIMP) to mask the height map data so that it's zero (black) outside the state boundary and at least slightly gray inside the state boundary. With OpenSCAD's surface, this would give you a rectangle that's flat outside the state and at some minimum height inside the state. You could then use one difference or intersection to cut across the model by height, trimming off the flat rectangular base.

(I.e., doing the trimming the image seems much easier than trimming an STL, & would totally work.)