The word set that completes the analogy spoon : stir are shovel : excavate, because the analogy is relating an object with his action.
The action that a spoon can accomplishment is stir and the action that a shovel can do is excavate.
If you note, the first word in the analogy is an object, the spoon and the shovel. And the second word in each analogy are the action related with that object, stir and excavate.
