Advisor is unhappy with M.Sc. research results and is showing signs of preventing the student from graduating. What should be done? I am having difficulties with an advisor who has not been clear with me on my research project, and I am fearful that I will not be allowed to graduate on time. What should I do? Please allow me to explain:
(Please note I am trying to be as vague as possible to conceal the situation and identities).
Previously, I was working at a company that was taking advantage of me, so me starting my M.S. was a ticket out of a bad work situation. I did not have many options to begin this program, and I really wanted to study this subject. So I began a M.S. program. The tough part of this situation was that I was introduced to a project right in the middle of it, so right from the start, it was rocky. There were probably less than 20 minutes devoted by the advisor to explaining the project to me, and it really wasn't set up for the kind of measurements that I was to take. It really wasn't set up for success to begin with, in my opinion.
The first year did not go well because of said reasons. Being more prepared the second year, I accomplished everything that the advisor wanted me to. I was therefore not able to do it the first year, but with the second year, I was able to get significant results. This work was to be included in a M.S. thesis, but the professor wanted me to  produce work that could be published in a scientific journal. However, in my area of study, it is not usually possible to publish results with only one year of data. The advisor did not like this, and is continuing to push me to analyze other kinds of data to try to make results that would be deemed publishable.
With this in mind, the data that I did collect makes a good thesis chapter. The original objective that was only briefly explained to me was accomplished, with results that showed the success of my experiment. However, knowing that I may not be able to publish it, my professor is telling me that what I have as a thesis article will not meet the advisor's expectations for graduation. I am trying other means of data analysis, but am not getting significant results. These results are not pleasing to this individual.
This problem is further complicated because the professor will not give me clear directions on where to head with this project. Every time I ask for help, I get no clear answers, just papers sent to me that only partially relate to my project. I do think that if my thesis is not going to be considered 'good enough,' there needs to be specific suggestions for improving it. But there are none. To make matters worse, I have not been prioritized, having been blown off several pre-arranged meetings with no apologies. I just never get a clear answer, and I often feel afraid to approach this person.
I feel like I can defend my thesis chapter well, but I am concerned that this person will ask me a whole bunch of questions during my defense (might not be related to my thesis) that I will not understand just because they are upset at my insignificant results. The committee may deem me unfit to graduate if I'm not able to answer them. It is not a requirement to publish in a peer-reviewed journal to graduate, so I have not failed that expectation.
As I feel like I have been short-handed in this process with no direction provided, what steps can I take to get around this? I want to graduate, but I feel like politics may impede this. Has anybody ever heard of anything similar? Is there an appeal process that I could take, if I am not allowed to graduate?
Thank you for reading!
This is half of an answer.

Has anybody ever heard of anything similar?

Yes. Conflicts like this unfortunately is not uncommon, judging from what I have observed in only two universities.
Indeed, it appears to be more and more common.

Is there an appeal process that I could take, if I am not allowed to graduate?

Formal appeal process?  Yes. The process varies from department to department. You should be able to find it in your students' handbook.
However, this should be considered as a last resort ---
it is quite unlikely going to work if your goal is to graduate.
Looking at the bigger problem though,
it seems the most straightforward solution is just to work hard and get results that will be sufficient to meet the requirement (publishable). This will certainly solve your problem, and it is likely the most efficient way.
If that's not the kind of solution you are looking for, then first, you need an unbiased assessment of your work to determine if you actually did work that is sufficient for graduation. While you may feel you have done enough, you need to consider the possibility that you are not an expert yet, and your assessment may not be correct.  If you can find another expert who thinks your work is sufficient for graduation, you may have a case, otherwise, I'm afraid there is not much you can do (if your goal is to actually graduate).
I disagree with the first comment, I think it is quite dangerous to start with graduate program director or some kind of ombuds. This would indeed be the official channel, but if you do that, your chance working out a reasonable solution with your advisor will be greatly reduced.