Although no executions actually occur on stage, they're still an important part of the imagery in Mother Courage. In particular, Swiss Cheese's execution becomes an allegory for Jesus's crucifixion. Let's examine the clues.
First, as the drums roll to signal his execution, the stage directions indicate that it momentarily "grows dark" (III, 701). The gospels of Matthew, Mark, and Luke all report that when Jesus enters the sixth hour of his execution, it suddenly grows dark for the next three hours, during which time Jesus dies: "And when the sixth hour was come, there was darkness over the whole land until the ninth hour" (Mark 15:33).
Second, Mother Courage denies that she knows who Swiss Cheese is, both when the soldiers question her and when they later bring her his body for identification. This is reminiscent of Peter, one of Jesus's disciples who denies knowing him in order to escape persecution.
And finally, in case these details aren't convincing enough, there is the chaplain's song, The Song of the Hours, which he sings after Swiss Cheese is arrested. The song tells of the events leading up to and including Jesus's crucifixion.
So, what does it all mean? Take a look at Swiss Cheese's "Character Analysis" for a few insights.