I am wondering if the difference between "It is terrible." and "What it is, is it is terrible." can mostly be described in terms of transformations, grammatically. Is it a kind of cleft sentence?
Based on my research,"It is terrible" and "What it is, is it is terrible" are not examples of cleft sentences. The phrases do not have the structure of cleft sentences.
An it-cleft sentence has this structure: It Cleft sentences:IT + BE (+ NOT AND/OR ADVERB) + EMPHASIZED WORD/PHRASE + THAT (WHO) CLAUSE For example, Mike took Sally to the party on Saturday. It was Mike who took Sally to the party on Saturday. The emphasis is on the subject. The emphasis also varies.
An wh-cleft/pseudo-cleft sentence has this structure: WH- cleft sentences:WH- Clause + BE + EMPHASIZED WORD / PHRASE For example, Mike took Sally to the party. What Mike did was (to) take Sally to the party. The emphasis is on the action. In these sentence, WHAT means THE THING(S) THAT. The WH-clause must contain a verb. To highlight the action we uses a form of DO in the WH-clause. The highlighted phrase usually contains a bare infinitive or TO + INF. If the highlighted verb is in the continuous or perfect, the form of DO matches it. The boys are taking Sandy to the match. What the boys are doing is taking Sandy to the match.
Here are the links for your reference: http://en.wikipedia.org/wiki/Cleft_sentence#Types; http://web.educastur.princast.es/eoi/eoimiere/myweb/blog/wp-content/uploads/cleft_sentences.pdf
I hope this information helps you somehow.
"It is terrible" is a regular subject-verb-predicate clause. "What it is, is terrible" is a wh-cleft, or pseudo-cleft: see Wikipedia's page on clefts. The example you give, with the repeated "it is", is also a kind of pseudo-cleft, though a rather more complex one.
Transformational accounts of pseudoclefts certainly exist. Chapter 2 of this 1979 dissertation gives an overview of a few possibilities. A more recent discussion of clefts in general, from a generative perspective, can be found in this 2010 dissertation. I'm sure there's more information in those two than you need!
The second sentence, "What it is, is it is terrible," is an example of a rhetorical device not specific to English, the interrogative device.
"What it is, is" is a rhetorical answer: it answers the preceding rhetorical question, "What is it?" Spoken or unspoken, this preceding question pairs with the rhetorical answer to draw extra dramatic emphasis to the final word, "terrible," by using an overly complex way of presenting that word as a sort of "drum-roll" of staccatto mono-syllablic words leading up to it.
It is called "interrogative" because "what" is an interrogative.
The repeated phrase, "it is," provides further emphasis for "terrible" via consonance with its "t."
I feel like this usage is likely to be employed by USA'n sports broadcasters (not saying "American" because I don't want to imply Canadians might resort to these sorts of barbaric implements).
See this article for discussion.