This is from the third act, when Catherine agrees to accompany Petkoff outside to help him deliver the orders. Petkoff wants to give the appearance that he will carry out Bluntschli's instructions with brisk self-confidence, but as he thinks it over, he seems aware of his inadequacy:
PETKOFF [officiously] Quite right, Bluntschli, quite right. I'll see to it. [He goes to the door importantly, but hesitates on the threshold]. By the bye, Catherine, you may as well come too. They'll be far more frightened of you than of me.
And Catherine uses the term "sputter" in response:
CATHERINE [putting down her embroidery] I daresay I had better. You would only splutter at them. [She goes out, Petkoff holding the door for her and following her].
The usage here refers to "sputtering" in the sense of saying something "rapidly, indistinctly, and with a spitting sound, as a result of anger, embarrassment, or another strong emotion" (Oxford English Dictionary).
Catherine knows her husband well, and can anticipate that he will feel too sheepish or awkward to speak to the men in the way that Bluntschli recommends. Earlier in the play, in his first conversation with Catherine, we've gotten a feeling for their relationship: She pressures him to take a more aggressive, active role, and he -- a naturally unambitious man who would prefer to avoid conflict -- protests that matters are beyond his control. ("Over my head, if you please," he says regarding Sergius's inability to get a promotion that Catherine thinks he deserves.)
In Act II, we've also been shown an example of Petkoff spluttering with irritation in response to Nicola's apparently bizarre behavior with the carpet bag.
PETKOFF [testily] First he shews Captain Bluntschli out here when he knew quite well I was in the--hum!--library; and then he goes downstairs and breaks Raina's chocolate soldier. He must--[Nicola appears at the top of the steps with a carpet bag. He descends; places it respectfully before Bluntschli; and waits for further orders. General amazement. Nicola, unconscious of the effect he is producing, looks perfectly satisfied with himself. When Petkoff recovers his power of speech, he breaks out at him with] Are you mad, Nicola?
So Catherine's pronouncement seems very apt. Petkoff is not likely to issue the commands in the clear, deliberate, and confident way that is needed.