讨 at the beginning of the sentence An example from a dictionary:

"讨不讨厌呀！Isn't that annoying?"

The first 讨 usage isn't clear here, as for beginner. Is it a special grammar structure? Maybe even an accidental mistake in the dictionary? (in case it happens sometimes)

Partly reminds tag question, but then it probably should have been "讨厌不讨厌" not "讨不讨厌", I'm not sure how it is used with multi-character words.
"討厭不討厭？" is a substantially shortened version of "討厭？還是不討厭？"  


As you can see, it is quite wordy. In practicality, "討厭不討厭？"  is still one character too long. The standard practice is to shorten it down to "討(厭)不討厭?" (the shorter the better) 

Similarly:


"明白不明白？" is  always shortened to 明不明白？or even further to "明不明？"
"知道不知道？" is  always shortened to 知不知道？or even further to "知不知？"


Avoid wordiness and omit as much as possible as long as the meaning is clear is consider good writing.