In modern Spanish both verbs ser and estar can be used with muerto.
Estar is used to describe the condition of being dead. The key is that the subject has not always been dead; the subject was alive sometime in the past. So, here being dead or alive is a transient condition. Other adjectives that depict a transient condition are vivo, enfermo, sano, preso, libre, soltero, casado, divorciado, viudo
El hombre está vivo
El hombre está sano
El hombre está libre
El hombre está casado
Examples like libre, soltero, casado, divorciado, viudo can also have the verb ser without changing the meaning.
El hombre es libre
El hombre es soltero
El hombre es divorciado
Sano can be preceded by the verb ser but the meaning is altered.
El hombre es sano (means that the man is healthy, not only is well but he probably has a healthy life that maintains him well)
With adjectives like muerto, casado, divorciado and sano (although with sano is somewhat weird) you can use tenses other than present to indicate that the new condition is initiated by the action of a third party.
Fue muerto a balazos
Serán casados por un ministro
Ha sido divorciado en dos ocasiones (correct but estado is more usual)
Y por su palabra fue sano (It's correct but somewhat archaic)