My father should have had surgery for cancer.

Literal

Father [topic-は] cancer surgery [object-を] receive-should was [despite-のに].

~べきであったのに expresses unfulfilled past obligation with regret: 'should have done X, but didn't.' べき marks the obligation, であった puts it in the past, and のに adds frustration or regret that it didn't happen. A heavy sentence about a missed medical opportunity.