I did a quick check and splitting at Peterborough and York (advance tickets on each leg) might save you £20 compared to the through ticket, but you would need to check exact timings to see how they could mesh together, as the cost of each leg varies throughout the day.
Try splitting at Peterborough and York.
There are £9 Advances from Norwich to Peterborough, £17.20 Advances on some trains from Peterborough to York and £9-11 Advances on some trains from York to Newcastle. Book from the East Coast website. I can't be more specific without knowing times of travel.
EDIT: Looks like I was beaten to it, but I will emphasise that booking on the East Coast website will save you money on the ticket from Peterborough to York as East Coast offer a roughly 10% online discount on most of their Advance fares.