Why Did Cersei Executes Missandei?

By killing Missandei she achieves her aim (to provoke Dany), keeping her alive is only helpful if she wants to avoid a fight.

Why did Cersei kill Missandei?

When Missandei dies, beheaded by the Mountain on Cersei's orders, it's in the hopes of provoking Daenerys into rash, violent action. ... She believes in Dany's mission of freeing slaves, but is often the voice of reason when it comes to escalating violence. We know that she loved Grey Worm and that he loved her.

How did Cersei get Missandei?

During Euron's ambush on Dany's fleet, her best friend and longtime servant Missandei is captured. She becomes Cersei's prisoner, and in the episode's final scene, Cersei orders the Mountain to behead her while Dany and Grey Worm are forced to watch. It's not pretty.