Is it acceptable as referee to contact an author on a paper you review? I am reviewing the second revision of a paper and am getting tired of this incredibly slow process of me pointing something out that requires clarification just to hear back from those authors two or three months from now (at the earliest).

Do you think I would insult gravely the academic spirit and / or authors of that manuscript if I just e-mailed the corresponding author saying "Look I still don't understand X because of Y can you please explain?"?

Personally, I think that doing so would just be what science is about: a bunch of people interested in similar scientific topics talking to each other.
I am reviewing the second revision of a paper and am getting tired of this incredibly slow process of me pointing something out that requires clarification just to hear back from those authors two or three months from now (at the earliest).


You don't need to e-mail the authors directly to get the information you want.  The several month delay you are talking about is the time it takes to collect all the reviews, send them to the authors, and wait for a revised version of the paper.  However, in the journals I'm familiar with you could request clarification by asking the editor to send a short message to the authors now and relay the response to you.  Going through the editor might slow things down by a day or two, but not by months.


  Do you think I would insult gravely the academic spirit and / or authors of that manuscript if I just e-mailed the corresponding author saying "Look I still don't understand X because of Y can you please explain?"?


The phrasing of your question is hyperbolic, but yes, this is something that could be considered offensive or unethical.  Sending queries through the editor slows things down only slightly, while it avoids various difficulties:


Reviewers might bypass the editor on requests they would rather not call to the editor's attention (for example, suggesting that their papers be cited).  Along similar ethical lines, announcing to the authors that you are reviewing their paper might help you pressure them for favors elsewhere.  For example, it would be unethical to write "Dear X, I'm a reviewer for your recent submission to Y.  I'm having trouble understanding it, so I fear it might take a while to arrive at a decision, but it could help to know blah blah blah.  Can you supply any additional information?  Regards, Z  P.S. Have you reached a decision about participating in the joint project I proposed?"
It's important for the editor to be aware of all relevant information.  If several reviewers request clarification about something, then that is itself informative about the clarity of the manuscript, even if they all agree in the end that it is correct.  It's also valuable for the editor to see and judge the response itself (and not just to know whether it convinced the reviewer).


As Daniel Shub pointed out in the comments, you can always ask the editor whether it would be appropriate for you to contact the authors directly (it may depend on journal policy, customs in your field, or the editor's judgment of the particular situation).  If the answer is yes, then you are all set.  However, if the answer is no or you don't ask, then you should relay all communication through the editor, and I would expect that to be the usual answer.