Does anyone know the word for a question asked with the intent to injure or insult?

What you're wanting here is either epiplexis:

Asking questions in order to chide, to express grief, or to inveigh. A kind of rhetorical question.

Examples

Why died I not from the womb? why did I not give up the ghost when I came out of the belly? —Job 3:11

or erotema:

The rhetorical question. To affirm or deny a point strongly by asking it as a question.

Generally, as Melanchthon has noted, the rhetorical question includes an emotional dimension, expressing wonder, indignation, sarcasm, etc.

Examples

Just why are you so stupid?

(Both those are from BYU's whipass Silva Rhetoricae)

The example you gave is of a loaded question, a suggestive question or a presuppositional question. It also offers the speaker's interlocutor a false dilemma.

(Links are to definitions and explanations of these terms in Wikipedia.)

I don't know that there is a single word to describe this. You might call it a dysphemistic question.

Dysphemism

The particular example question might fall under Aporia (though the term doesn't apply strictly to questions, but you could talk about an aporetic question). Quotes from OED:

1589 G. Puttenham Arte Eng. Poesie iii. xix. 189 Aporia, or the Doubtfull. [So] called..because oftentimes we will seeme to cast perils, and make doubt of things when by a plaine manner of speech wee might affirme or deny him.

1656 J. Smith Myst. Rhetorique 150 Aporia is a figure whereby the Speaker sheweth that he doubteth, either where to begin for the multitude of matters, or what to do or say in some strange or ambiguous thing.

However, aporia doesn't have to be used in service of insult.