Could we also say "min morfar nyligen dog"?
No, because in normal Swedish sentences (= not questions or subclauses), the verb must be in second place. min morfar takes up the first place, so you must have the verb as the next thing.
I used "farfar" instead of "morfar". What's the difference?
One is your father's father (farfar) and the other is your mother's (morfar)
Varför funkar "min morfar dog nyss" inte?
nyss is more like "just now". It only really works if your grandfather died something like a few minutes ago.