Answer: That's a good question, and the answer is probably to be found somewhere in the history of the Spanish language rather than in any logical application of the rules of grammar. To the native Spanish speaker, ser and estar are two separate verbs, seldom interchangeable. But because they can both be translated as "to be," they have been the source of confusion over the years to English speakers learning Spanish as a second language.
If grammar were only a matter of following rules, one could make good arguments for using either ser or estar. Rather than list opposing arguments (which would probably serve more to confuse than anything else), I'll mention just two related rules that make a good case for using estar.
First is that when a form of ser is followed by a past participle, it generally refers to the process of a verb's action taking place, while estar followed by a participle generally refers to a completed action. For example, in los coches fueron rotos por los estudiantes (the cars were broken by the students), fueron rotos passively refers to the action of the cars being broken. But in los coches están rotos (the cars are broken), the action has been completed.
Similarly, the use of estar generally suggests there has been a change. For example, tú eres feliz (you are happy) suggests the person is by nature happy, while tu estás feliz (you are happy) suggests that the person's happiness represents a change from a previous state.
Following either of these guidelines for choosing the right "to be" would result in the use of a form of estar in a sentence such as mi padre está muerto.
As I mentioned earlier, one might also come up with arguments for using ser, and ser is often the choice incorrectly made by beginning Spanish students. But the fact is that estar is used with muerto, and it is also used with vivo (alive): Mi padre está muerto, mi madre está viva. (My father is dead, my mother is alive.)
All logic aside, the indisputable rule that estar is the verb of choice with muerto is just something you'll have to remember. That's just the way it is. And after a while, estar is the verb that will sound right.