You can absolutely resharpen carbide inserts but you need a good diamond wheel to do it, like an Accu-Finish machine. I have one and have sharpened and tuned up inserts BUT you cannot refresh a broken off, trashed insert like you show in the pics. The best thing to do is first, figure out why you trashed the insert the way you did and two, buy better inserts. Seco, Iscar, Kennametal all sell CCGT inserts like you're showing but the quality is far better. The Kyocera inserts are commonly not real Kyocera inserts; they're Chinese copies. While they work, they do not work well or for nearly as long.