I would use a mucking fork with at least 10 tines, it works great for digging into the soil and filtering out long strands of root material and other trash. It looks like a stubby pitchfork with a D handle, and many more tines. I use this method for small jobs like getting rid of johnson grass rhizomes in freshly turned soil. Turn the fork over and use it as a rake to collect what you have lifted to the surface. Always works fine for me. I can't think of any other way that's more effective.
If the roots are coming from desirable shrubs you shouldn't be digging them up or disturbing them. Are you planning on planting in this area in the future(annuals,shrubs,etc). then add topsoil to this area. Or if no plants, are you going to mulch this area. I'm kinda confused about the Q?
To little info here. If the roots are from a maple tree or shrubs and they are on the upper surface then there is more of problem here then removing the roots. Is this an existing bed that has gone fallow? I know a little of the topography in your area and its high in sand content is it not? Need more info or maybe a pic.