How do I express sarcasm in non-dialogue text when writing a fiction novel?

Sarcasm is, almost by definition, dialogue. In fact, Merriam-Webster defines it as:

“I’m still not entirely clear on what you want me to do.”

“How?”

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“You see?” Spencer’s voice came. “My logic is beyond reproach. Iris is too important to the future of the Guild to risk. Dia and Janet likewise. The other students lack May’s outside perspective, so they are less likely to succeed. May is the right choice: expendable, but still just capable enough to make victory possible.”

A moment later, the barrage ended. The dome, now considerably smaller than it had been, faded from view. That sense of presence returned to the statue. “I’m terribly sorry.” Spencer’s voice sounded thinner, somehow, weaker in May’s ears. “This situation is an intolerable nuisance. May, I wonder if we might impose on you to help save Serene’s life and ensure the future of the Guild? I wish I could say you’ll be fine, but I’m afraid the odds are rather good that you’ll die.”

“Think of something. Make it good, or all is lost.”

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“Did you know they would try to grab me?”

“But I can,” May said. “You helped me out when I was in a bind, and you didn’t even know me. Besides, Spencer’s right.”

Cambridge Dictionary concurs:

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I’m…hmm. I’ve seen this question float through my feed a couple of times now, and I’m still not quite sure I understand what you’re asking.

Serene’s face hardened. “I see. In any event, as long as he remains connected to it, I cannot escape. You need to break his connection.”

May jumped. “Don’t sneak up on a girl like that! You almost scared me out of my skin.”

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“In that case, lemme have it.”

“So sorry to disturb you,” Spencer said. “I thought you’d want to be informed of potential threats ahead. If I’ve misjudged, please don’t hesitate to let me know.”

“No.”

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“What do you need me to do?” May said.

“I cannot see the future.” A hint of impatience coloured Spencer’s voice. “At the moment, I think the task at hand is rather more pressing than the past.”

“Good luck.” Serene stood. They embraced for a moment, then the air sizzled, the diagram flared, and May found herself standing, shuddering and queasy, at the foot of the skyscraper. She set out down the street in the strange twilit gloom of Spencer’s imaginary London, toward the scribble of the Thames and the sinister whirligig of the London Eye.

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a sharp and often satirical or ironic utterance designed to cut or give pain.

“Ah, of course. Listen, this is your space, or alternate reality, or dream, or whatever the hell it is, right? You’ve already zapped me around from place to place. Why am I hoofing it to wherever it is I’m going?”

May stared down at her mug, half-expecting to see some strange brew of raw magical essence. Ordinary tea filled an ordinary china cup. She took a deep breath, then swallowed the liquid. Nothing in particular happened. “Thank you,” Spencer said. “Now, off you go.”

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Spencer sighed, the sound coming from the air itself. “It’s not really tea, of course. It’s the tangible representation, within this space, of a spell. Specifically, a spell that will allow you to communicate with Serene from wherever you are, among other things.”

So I’m not sure that you can have “sarcasm in non-dialogue text,” as sarcasm is generally defined in terms of something you say or express…or perhaps I’m just not getting what you’re trying to ask.

“I can answer that,” May said. “They’ve already used most of that energy for something else. We still don’t understand exactly what. A directed spell of some sort, focused through a human sacrifice.”

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“Right. The Eye. Why can’t you just teleport me there?”

“Oh, I get it! You’re being snarky.”

“Right. Okay. Focus.” She hurried along, trotting through the London that was not London, surrounded by phantasmagorical impressions of people that flitted around her in silence. “So how does this work? Is this, like, a real-time simulation? Are those weird blurs actually people in the real London right now? If someone were walking down this street in real London, would they see people where I see those—whatever they are?”

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“You could at least try to sugar-coat it a bit,” May grumbled.

“May,” Serene said, “I can’t—”

“I hardly think this is the time for a lesson on the mathematics of planar resonance in advanced multidimensional thaumaturgy.”

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Serene raised her hand. “I don’t think this is a good—”

“I’m a cat.”

“Fine.” May rose from the small table. “The hard way it is.”

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“There are currently some…complications. The Adversary has created a significant intrusion into this space, territory they control. Their presence is, and I do not say this lightly, quite painful. I have done the best I can.”

“Yes?”

“So hey, about that.” May followed the street along the bank of the river. Strange blurred figures walked along the sidewalk with her, looming threateningly over her, dim and amorphous save for their hands and legs. She shivered as she made her way around them. In the street, suggestions of cars screamed by, much too fast, as vague and indistinct as the walking figures except for the noise and stench they left in their wake. “That night you followed me home from the club…”

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“Ah, forgive me once again. May, I would consider it a personal favour if you might consider doing a small task for me.” Spencer’s voice carried a note of supercilious sarcasm. “You might not die.”

“If you must know,” Spencer said in a tone that suggested she didn’t, “it will allow Serene to see through your eyes and utilise you as a conduit for her spellcasting abilities. If you please.”

“Can’t you just, like, blink me directly to where I need to be?” May said.

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“Good heavens.” Annoyance touched Spencer’s voice. “We can’t be expected to figure out everything! You’ll have to work that bit out. Please, drink your tea.”

“The Adversary has placed sentries of a sort,” Spencer’s voice announced, “which I expect will grow more numerous as you get closer.”

the use of remarks that clearly mean the opposite of what they say, made in order to hurt someone's feelings or to criticize something in a humorous way

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“What?”

“Lord Dormer is personally overseeing this attack on my mind,” Serene said. “He appears to be directly coupled to the accumulator. I do not know why he is not using more of the stored power within it.”

“What other things?”

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In our upcoming novel London Under Veil, Eunice and I have a character who’s quite sarcastic:

“I didn’t realise you were so sarcastic.”

“The Eye.”

I’m not really sure how you’d convey sarcasm without dialogue, since sarcasm is, by its nature, intrinsically wedded to dialogue. It’s a form of expression.

“Okay, okay, you don’t have to rub it in.” May ran a hand through her hair. “What do I need to do?”

“Ordinarily I would say yes, but as the Adversary continues to gain ground in this space, I find myself increasingly constrained. I fear you will need to make your own way.”

“Your objection is noted,” Spencer said. “If we may move on to the important bit of this conversation, I would be appreciative if you might make your way over to the Eye and see if you might sabotage or otherwise distract our opponents long enough for Serene to shake off this bothersome spell that’s trying to eat its way into her mind. I would do it myself, but as you can see, I’m a bit busy maintaining this place and limiting the Adversary’s access, though I will confess to some consternation at the effectiveness with which they’ve made their way in. It must be convenient to have access to a source of energy more powerful than anything ever recorded in the history of magic. Crude, our opponents, but highly effective. Anything can be weaponized if you put enough force behind it.”

“I am, as I believe we have established already, a cat.”

“Advanced what?” She picked up speed, finding as she raced along the sidewalk that her legs didn’t tire, her lungs didn’t burn. “Is that a thing?”