As Rodan attempts to kill Mothra, she stabs him through the left shoulder, incapacitating him for the duration of the battle between Godzilla and Ghidorah. After Godzilla kills Ghidorah, Rodan and the other Titans acknowledge Godzilla as their new alpha by bowing down to him.

Did Mothra really die?

Mothra is an immortal deity, and despite having died multiple times she is always reborn through her egg. Mothra has protected the planet many times from monsters like King Ghidorah and sometimes has been put in conflict with Godzilla.

How did Rodan survive Mothra?

Rodan survived being completely impaled by Mothra's stinger, the attack only temporarily incapacitating him before he recovered virtually unharmed despite the gaping wound in his chest. However, he was quickly dispatched in battle by King Ghidorah, who used a single Gravity Beam as his finishing blow.