What is the linguistic term to describe “–“ part of the phrase in “He ‘lied his a– off”?

Washington Post (December 6), carried an article under the headline, “He ‘lied his a– off : Carrier union leader on Trump’s big deal” which is followed by the following paragraph;

“At the Dec. 1 meeting, where Trump was supposed to lay out the details, ones hoped he would explain himself. “But he got up there,” Jones said Tuesday, “and, for whatever reason, lied his a-- off.”

I instantly realized what "a- off" mean, but I’m curious to know what do you call the “—“ part of the word in English, and how do you vocalize when you read it out. Do you read it, like "a-blah-blah - off"?

We call it “伏字” – meaning “hidden characters” in Japanese. Obviously it’s different from “expletive” which consists a whole word, not a part of it.

Though Readers Japanese English Dictionary published by Kenkyusha renders “an omission / blank / turn” as English counterparts to “伏字,” I’m not sure whether it applies to “a-off” case.

it's called a strike-through, a partial strikethrough or a censored text. it's a censored profanity or vulgarity, a crossed out word, text that has been filtered. It's an unofficial notation to depict censorship used by some magazines. In older newspapers they sometimes used (expletive) instead of a--.

Previous to the advent of PC's, censored profanites and phrases in reports were barred with a pen or with a large black marker, with two oblique lines or some such lines.

Probably the language hasn't had the time or requirement to find a specific term for censorship of computer glyphs, as a strikethrough is nearly the same as a crossed out word or a censored text.

There's probably a figure of speech referring to sanitization... of a text or vulgarity, to represent profanities that have been processed by an editor to be printable. Sanitization of text and glyphs is a used term, i.e. here: https://tex.stackexchange.com/questions/165139/black-marker-effect-in-the-text-sanitization-used-to-hide-passwords-in-code-e

A related censorship notation is this trick from comics and television is symbol swearing: "^%$#&"

The term used in English for the dash in 'a—' is widespread (that is, the term is not confined to linguistics). The same term is used for "what" it is called and "how" it is vocalized ("what do you call the '—' part of the word in English, and how do you vocalize when you read it out"); because of this duality, in part, defining the term is difficult — like taking a hole out of the pocket it's in so you can examine it more closely.

The best approach to answering your question seems to be to quote the (confusing) entry for the term in OED Online, where it is attested in more general use (12a) since 1773, and in the specific euphemistic use (12b) since 1854:

blank, n.
12.
a. A dash written in place of an omitted letter or word. Thus, —— —— Esq. of —— Hall, read Blank Blank Esquire of Blank Hall. Cf. DASH n.¹

b. Used euphemistically as a verbal representation of a dash put instead of an oath or profane word.

["blank, n.". OED Online. December 2016. Oxford University Press. http://www.oed.com/view/Entry/19884?rskey=lfbPzj&result=1&isAdvanced=false (accessed December 11, 2016).]

That OED entry cross-references 'dash', because that is the name of the type of symbol (the 'glyph', here used in the sense of "any symbol bearing information nonverbally, as a crossed-out cigarette on a no-smoking sign", Random House) commonly used to represent what is called the blank.

The functional name of the blank, as opposed to the name of the symbol used to convey it, is 'blank', and it is vocalized as that.