Is it correct to use quotes before a comma when not representing spoken text?

Quotation marks are sometime used:

- to draw attention to a word;

- to indicate an unusual use of a word;

- to suggest that the writer want to be distanced from word.

The comma and the question mark come after the quotation marks in such cases.

In this light, the sentence

Should I say "stand up", "standup", or "stand-up"?

is perfectly valid.

Instead, the sentence

Should I say "stand up," "standup," or "stand-up"?

is not valid because, although the question mark came after the quotation marks (... or "stand-up"?), the comma does not allow the rule I have mentioned.¹

¹ For more explanations and examples see Collins Easy Learning - Grammar and Punctuation, to which I am referred to for answering the question you have asked.

It depends from which language you are using to write. For example, in American English the comma following the quoted part is written inside the quotes, as reported from Comma Sense—A fun-damental guide to punctuation (by Richard Leederer, and John Shore), which says:

In U.S. punctuation, periods and commas always—and we do mean always—go inside the quotation marks.

Some of the examples found in the book are the following ones:

In "Confessions of an Alliteration Addict," the lead article in the August 2005 issue of Neurosis Today, Edema Edington recounts a childhood in which she was force-fed storied and rhymes about Jack and Jill, Simple Simon, Miss Muffet, King Cole, Boy Blue, Red Riding Hood, Peter Peter Pumpkin Eater, and Georgie Porgie Pudding and Pie.

"I really zapped Aloysius," boated Edema.

The word "politics" derives from two ancient roots: "poly," meaning "many," and "tics," which are blood-sucking parasites.

The comma is placed inside the quotation marks, whatever you are using them to report what has been said from somebody, or you are using quotation marks to distinguish words-as-words.

In the latter case, you could write the sentence as follows:

The word "politics" derives from two ancient roots: poly, meaning "many," and tics, which are blood-sucking parasites.

As a side note, the comma is not used inside the quotation marks, if the quotation ends with a question mark, or an exclamation point.

"You lie!" answered Edema.
"No I don't" risposted Aloysius.

"What happened to Aloysius?" she asked.