Suppose that,during a conversation in a book, one character says something sarcastically. As the author, I want the readers to know that the character was being sarcastic, but I do not want to say the phrase "said sarcastically."
An example is below:
"I'm glad to know that's what you think of my politics," Andrew said sarcastically.
Is there a single word that I can use to replace the phrase "said sarcastically"?
Something I've found is that when you're trying to replace a phrase of the form "said Xly", there often isn't a single verb that does the job. I've come to see this as a potential warning sign that there is too much information being packed into the adverb, or that it isn't a good descriptor for verbal speech, and I need to revisit the whole phrase to see how I can more naturally get that concept across.
Often, this means rewriting it to be more descriptive. I am a huge fan of dialog tags that aren't explicitly verbal for this purpose.
In your specific example, I'd probably consider going for:
"I'm glad to know that's what you think of my politics." Andrew rolled his eyes.
or some other bit of gesture or body language that conveys the sarcastic nature of the response. This has the advantage that you're bringing in more physicality, especially if you expand on the snippet with physical action.
If Andrew is the POV character, there's also options like:
"I'm glad to know that's what you think of my politics." He didn't even know why he bothered trying sometimes.
Also, especially for things like sarcasm, often the dialogue in and of itself can be made clear enough that the tag is redundant:
"Wow. I'm glad to know that's what you think of my politics."
"Oh come on, you know I didn't mean it that way!"
TL;DR version: There isn't one, so try things beyond simple one-for-one replacement.
"I'm glad to know that's what you think of my politics," Andrew scoffed.
To scoff is to speak derisively or contemptuously. It is less strong than "mocked" or "sneered".
Avoid the adverb ("sarcastically") even if it costs you more words. Even if it costs you a paragraph.
A huge mistake of beginning writers is that they think they need to compress their writing, and adverbs help them do that. What they fail to understand is that readers of fiction do not mind reading. You don't have to get your point across quickly or in the minimum number of words!
The job of the fiction writer is to guide the imagination of the reader, in the visual, auditory, sensory and emotional realms, so the reader sees, hears and feels what the writer is imagining for the characters.
You do need to pick out the highlights that matter, but describe those. If Andrew's tone of voice is "sarcastic",
David was dismissive. "That's just stupid."
Andrew mustered all the sarcasm he could. "I'm glad to know what you think of my politics, David! That's very insightful input."
Don't worry about word counts. Avoid the adverbs if you can. Guide the reader's imagination, that is the point.
You should have a movie going on your head, but you don't have the film maker's camera for the imagery, or music to clue us into the emotions, or the voices to convey the tones of voice. You must use words to convey all of the critical details to the reader.
The readers are not in a hurry to finish your story; but they will put it down if you fail to guide their imagination.
This is why we warn against "talking heads", and adverbs: They fail to prompt the imagination.
I'd also suggest that when tone of voice is important, it precede the speech (so it will be read in the correct tone), not follow it.
In some cases "he said sarcastically" can be replaced by "he snarked".
I just checked and snark is used as both a noun and a verb.
https://www.merriam-webster.com/dictionary/snark
Thus in some cases "snarked" can be used instead of "said sarcastically".
Sneered or smirked actually describes a facial expression, but conveys the sarcasm too. Some other possibilities: quipped, mocked, scoffed, or japed.
But what you probably want to do is give a description that shows what the character is really saying. You want to paint a vivid picture anyway!
Unfortunately, there is no word that means "to declare, state, or say with sarcasm."
However, there are words that that can be used to communicate the meaning behind "said sarcastically." Some of these words are "mocked," "sneered," "taunted," and "snarled." Using these words, the sentence becomes
"I'm glad to know that's what you think of my politics," Andrew mocked.
"I'm glad to know that's what you think of my politics," Andrew sneered.
If these words are too harsh for the context of the conversation, you can use another phrase to communicate sarcasm:
"I'm glad to know that's what you think of my politics," Andrew sighed.
"I'm glad to know that's what you think of my politics," Andrew lamented.
In the end, you will need to decide which of the words best fit the broader conversation. But these examples should save you from having to use the awkward phrase "said sarcastically."