I confess that I have not read all replies in detail, so the following may not make sense depending on exactly how the intersection geometry was generated. Are there are edges shared between the wanted section and the waste section? If so, don’t delete them. Only delete the edges that are purely part of the waste section, not part of the wanted section (e.g., edges that project beyond the intersection/cutting plane). You might have to select such edges one-by-one, or perhaps a careful selection box will get many of them together.
Keep in mind that a left-to-right selection box only selects entities that are entirely contained within the box, whereas a right-to-left selection selects all entities which are visible in the box. Use whichever form might be most suitable.