Select the object to cut,, make sure its in object mode. Get your Cut Faces tool, click the center of the boue line, swing it out, then turn it so you have it angled right, and let go.

EDIT: I think your wanting to do it more perfect? You could get your split polygon tool, and cut if face by face, so its perfect. This 'snaps' Not sure exactly what you want, your very unclear.